Differentiation Formulas List

English Mathematics
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Differentiation Formulas List?

Differentiation Definition: Let’s say y is a function of x and is expressed as y=f(x). Then, the rate of change of “y” per unit change in “x” is given by \frac{dy}{dx},

\frac{dy}{dx}={f}'(x)

Differentiation Formulas for Trigonometric Functions

1. \begin{array}{l}\frac{d}{dx} (sin~ x)= cos\ x\end{array}

2. \begin{array}{l}\frac{d}{dx} (cos~ x)= – sin\ x\end{array}

3. \begin{array}{l}\frac{d}{dx} (tan ~x)= sec^{2} x\end{array}

4. \begin{array}{l}\frac{d}{dx} (cot~ x = -cosec^{2} x\end{array}

5. \begin{array}{l}\frac{d}{dx} (sec~ x) = sec\ x\ tan\ x\end{array}

6. \begin{array}{l}\frac{d}{dx} (cosec ~x)= -cosec\ x\ cot\ x\end{array}

7. \begin{array}{l}\frac{d}{dx} (sinh~ x)= cosh\ x\end{array}

8. \begin{array}{l}\frac{d}{dx} (cosh~ x) = sinh\ x\end{array}

9. \begin{array}{l}\frac{d}{dx} (tanh ~x)= sech^{2} x\end{array}

10. \begin{array}{l}\frac{d}{dx} (coth~ x)=-cosech^{2} x\end{array}

11. \begin{array}{l}\frac{d}{dx} (sech~ x)= -sech\ x\ tanh\ x\end{array}

12. \begin{array}{l}\frac{d}{dx} (cosech~ x ) = -cosech\ x\ coth\ x\end{array}

Formulas for Inverse Trigonometric Functions

  1. \begin{array}{l}\frac{d}{dx}(sin^{-1}~ x)=\frac{1}{\sqrt{1 – x^2}}\end{array}

  2. \begin{array}{l}\frac{d}{dx}(cos^{-1}~ x) = -\frac{1}{\sqrt{1 – x^2}}\end{array}

  3. \begin{array}{l}\frac{d}{dx}(tan^{-1}~ x) = \frac{1}{1 + x^2}\end{array}

  4. \begin{array}{l}\frac{d}{dx}(cot^{-1}~ x) = -\frac{1}{1 + x^2}\end{array}

  5. \begin{array}{l}\frac{d}{dx}(sec^{-1} ~x) = \frac{1}{|x|\sqrt{x^2 – 1}}\end{array}

  6. \begin{array}{l}\frac{d}{dx}(cosec^{-1}~x) = -\frac{1}{|x|\sqrt{x^2 – 1}}\end{array}

Logarithmic function Differentiation Formulas

  1. \begin{array}{l}\frac{d}{dx}(a^{x}) = a^{x} ln a\end{array}

  2. \begin{array}{l}\frac{d}{dx}(e^{x}) = e^{x}\end{array}

  3. \begin{array}{l}\frac{d}{dx}(log_a~ x) = \frac{1}{(ln~ a)x}\end{array}

  4. \begin{array}{l}\frac{d}{dx}(ln~ x) = 1/x\end{array}

Chain Rule:

\begin{array}{l}\frac{dy}{dx}= \frac{dy}{du}\times \frac{du}{dx}= \frac{dy}{dv}\times \frac{dv}{du}\times \frac{du}{dx}\end{array}

:white_check_mark: :point_right:t3: List of Trigonometry Formulas PDF | Sorumatik

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What are the basic rules of differentiation?

Power Rule: (d/dx) (xn ) = nx{n-1}
Sum Rule: (d/dx) (f ± g) = f’ ± g’
Product Rule: (d/dx) (fg)= fg’ + gf’
Quotient Rule: (d/dx) (f/g) = [(gf’ – fg’)/g2]

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Basics Differentiation Formulas

  1. \frac{d}{dx} (k)= 0

  2. \frac{d}{dx} (ku)= k\frac{du}{dx}

  3. \frac{d}{dx} (u±v)= \frac{du}{dx}±\frac{dv}{dx}

  4. \frac{d}{dx} (uv)= u\frac{dv}{dx}+v\frac{du}{dx}

  5. \frac{d}{dx} (u/v)= \frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}

  6. \frac{dy}{dx}.\frac{dx}{dy}= 1

  7. \frac{d}{dx} (x^n)= nx^{n-1}

  8. \frac{d}{dx} (e^x)= e^x

  9. \frac{d}{dx} (a^x)= a^x\log a

  10. \frac{d}{dx} (\log x)= \frac{1}{x}

  11. \frac{d}{dx} \displaystyle \log _{a}x= \frac{1}{x}\displaystyle \log _{a}e

  12. \frac{d^n}{dx^n} (ax+b)^n= n!a^n