Basic Calculus handwritten notes pdf in English

Hello aspirants,
Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. It is used to solve problems in a wide variety of fields, including physics, engineering, economics, and statistics. In calculus, the basic concepts of differentiation and integration are used to study functions and their properties. Differentiation is the process of finding the rate of change of a function with respect to one of its variables, while integration is the process of finding the area under a curve. Calculus is also used to study the behavior of functions near infinity, as well as the behavior of functions that are not continuous.

Calculus is a branch of mathematics that deals with the study of derivatives, integrals, and functions. It is used to analyze the behavior of functions, such as their rate of change and their area under the curve. Calculus is essential for understanding more advanced topics in mathematics, such as differential equations and numerical analysis. Derivatives are used to measure the rate of change of a function. This can be done by taking the limit of the ratio of the change in the function to the change in its input.

Integrals are used to measure the area under a curve. This can be done by taking the limit of the sum of the areas of the rectangles under a curve. Functions are mathematical objects that map input to output. They can be linear, polynomial, exponential, or logarithmic. Functions can be used to model real-world phenomena, such as population growth or the motion of a particle.

Calculus is an important tool in physics, engineering, economics, and many other disciplines. It can be used to solve a variety of problems, from finding the maximum or minimum of a function to calculating the motion of a particle. It is also used to solve problems in calculus-based fields such.

Download GK Notes

Basic Calculus

Calculus is the mathematical study of change. It is used to describe the behavior of functions and is used in a variety of fields, including engineering, economics, and physics. Calculus is divided into two parts: differential calculus and integral calculus.

Differential calculus is the study of how functions change over time. It deals with derivatives, or the rate of change of a function, and is used to calculate slopes, tangents, and maxima and minima.

Integral calculus is the study of how functions are accumulated over time. It deals with integrals, or the area under a curve, and is used to calculate distances, volumes, and areas.

Calculus can be used to solve problems in real-world applications, such as motion, optimization, and growth. It can also be used to study and predict the behavior of complex systems, such as the weather and the stock market.

Most Important Basic Calculus Question Answer

Q 1. Find the derivative of $f (x) = 6 x^{3} - 9 x + 4$ .

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

f^{'} (x) = 18 x^{2} - 9

Q 2. Find the derivative of

y = 2 t^{4} - 10 t^{2} + 13 t

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

\frac{d y}{d t} = 8 t^{3} - 20 t + 13

Q 3. Find the derivative of $g (z) = 4 z^{7} - 3 z^{- 7} + 9 z$ .

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

g^{'} (z) = 28 z^{6} + 21 z^{- 8} + 9

Q 4. Find the derivative of $h (y) = y^{- 4} - 9 y^{- 3} + 8 y^{- 2} + 12$ .

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

h^{'} (y) = - 4 y^{- 5} + 27 y^{- 4} - 16 y^{- 3}

Q 5. Find the derivative of $y = \sqrt{x} + 8 \sqrt[3]{x} - 2 \sqrt[4]{x}$ .

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that you’ll need to convert the roots to fractional exponents before you start taking the derivative. Here is the rewritten function.

$y = x^{\frac{1}{2}} + 8 x^{\frac{1}{3}} - 2 x^{\frac{1}{4}}$ The derivative is,

$\frac{d y}{d x} = \frac{1}{2} x^{- \frac{1}{2}} + \frac{8}{3} x^{- \frac{2}{3}} - \frac{1}{2} x^{- \frac{3}{4}}$

More Related PDF Download

Maths Topicwise Free PDF > Click Here To Download	English Topicwise Free PDF > Click Here To Download
GK/GS/GA Topicwise Free PDF > Click Here To Download	Reasoning Topicwise Free PDF > Click Here To Download
Indian Polity Free PDF > Click Here To Download	History Free PDF > Click Here To Download
Computer Topicwise Short Tricks > Click Here To Download	EnvironmentTopicwise Free PDF > Click Here To Download
UPSC Notes > Click Here To Download	SSC Notes Download > Click Here To Download

Most Important Basic Calculus Question Answer

Q 6. Find the derivative of

f (x) = 10 \sqrt[5]{x^{3}} - \sqrt{x^{7}} + 6 \sqrt[3]{x^{8}} - 3

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that you’ll need to convert the roots to fractional exponents before you start taking the derivative. Here is the rewritten function.

$f (x) = 10 {(^{3})}^{\frac{1}{5}} - {(^{7})}^{\frac{1}{2}} + 6 {(^{8})}^{\frac{1}{3}} - 3 = 10 x^{\frac{3}{5}} - x^{\frac{7}{2}} + 6 x^{\frac{8}{3}} - 3$ The derivative is,

$f^{'} (x) = 10 (\frac{3}{5}) x^{- \frac{2}{5}} - \frac{7}{2} x^{\frac{5}{2}} + 6 (\frac{8}{3}) x^{\frac{5}{3}} = 6 x^{- \frac{2}{5}} - \frac{7}{2} x^{\frac{5}{2}} + 16 x^{\frac{5}{3}}$

Q 7. Find the derivative of

f (t) = \frac{4}{t} - \frac{1}{6 t^{3}} + \frac{8}{t^{5}}

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that you’ll need to rewrite the terms so that each of the $t$ ’s are in the numerator with negative exponents before taking the derivative. Here is the rewritten function.

$f (t) = 4 t^{- 1} - \frac{1}{6} t^{- 3} + 8 t^{- 5}$ The derivative is,

$f^{'} (t) = - 4 t^{- 2} + \frac{1}{2} t^{- 4} - 40 t^{- 6}$

Q 8. Find the derivative of

R (z) = \frac{6}{\sqrt{z^{3}}} + \frac{1}{8 z^{4}} - \frac{1}{3 z^{10}}

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that you’ll need to rewrite the terms so that each of the $z$ ’s are in the numerator with negative exponents and rewrite the root as a fractional exponent before taking the derivative. Here is the rewritten function.

$R (z) = 6 z^{- \frac{3}{2}} + \frac{1}{8} z^{- 4} - \frac{1}{3} z^{- 10}$ The derivative is,

$R^{'} (z) = 6 (- \frac{3}{2}) z^{- \frac{5}{2}} + \frac{1}{8} (- 4) z^{- 5} - \frac{1}{3} (- 10) z^{- 11} = - 9 z^{- \frac{5}{2}} - \frac{1}{2} z^{- 5} + \frac{10}{3} z^{- 11}$

Q 9. Find the derivative of

z = x (3 x^{2} - 9)

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that in order to do this derivative we’ll first need to multiply the function out before we take the derivative. Here is the rewritten function.

$z = 3 x^{3} - 9 x$ The derivative is,

$\frac{d z}{d x} = 9 x^{2} - 9$

Q 10. Find the derivative of

g (y) = (y - 4) (2 y + y^{2})

Ans. There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that in order to do this derivative we’ll first need to multiply the function out before we take the derivative. Here is the rewritten function.

$g (y) = y^{3} - 2 y^{2} - 8 y$ The derivative is,

$g^{'} (y) = 3 y^{2} - 4 y - 8$

Topic Related PDF Download

Download pdf

pdfdownload.in will bring you new PDFs on Daily Bases, which will be updated in all ways and uploaded on the website, which will prove to be very important for you to prepare for all your upcoming competitive exams.

The above PDF is only provided to you by PDFdownload.in, we are not the creator of the PDF, if you like the PDF or if you have any kind of doubt, suggestion, or question about the same, please send us on your mail. Do not hesitate to contact me. [email protected] or you can send suggestions in the comment box below.

Please Support By Joining Below Groups And Like Our Pages We Will be very thankful to you.

Facebook Page: https://www.facebook.com/onlyupsc/

Post Views: 383

PDF Download

Basic Calculus handwritten notes pdf in English