Subject: Calculus

Table Of Derivatives

The following are the most common and simplest forms of derivative and its answers.

The Page at a Glance

Derivative of ordinary functions

Simple Functions

1. D_{x}(u^{r}) = ru^{n-1}\cdot D_{x}u
2. D_{x}(u+v) = D_{x}u+D_{x}v
3. D_{x}(u\cdot v) = vD_{x}u+uD_{x}v
4. D_{x}(\frac{u}{v}) = vD_{x}u-uD_{x}v\over v^2


Derivative of ordinary exponential and logarithmic functions

Simple Logarithmic and Exponential Functions

1. D_{x}e^{u} = e^{u}D_{x}u
2. D_{x}a^{u} = a^{u} \ln{u} D_{x}u
3. D_{x}(\ln{u}) = \frac{1}{u}D_{x}u


Derivative involving trigonometric functions

6 Trigonometric Functions

1.D_{x}\sin{u} = \cos{u}D_{x}u

2.D_{x}\cos{u} = -\sin{u}D_{x}u

3.D_{x}\tan{u} = \sec^{2}{u}D_{x}u

4.D_{x}\cot{u} = -\csc^{2}{u}D_{x}u

5.D_{x}\sec{u} = \sec{u}\tan{u}D_{x}u

6.D_{x}\csc{u} = -\csc{u}\cot{u}D_{x}u


Derivative involving inverse trigonometric functions

Inverse trigonometric functions

1.D_{x}\sin^{-1}{u} = \frac{1}{\sqrt{1-u^{2}}}D_{x}u

2.D_{x}\cos^{-1}{u} = -\frac{1}{\sqrt{1-u^{2}}}D_{x}u

3.D_{x}\tan^{-1}{u} = \frac{1}{1+u^{2}}D_{x}u

4.D_{x}\cot^{-1}{u} = -\frac{1}{1+u^{2}}D_{x}u

5.D_{x}\sec^{-1}{u} = \frac{1}{u\sqrt{u^{2}-1}}D_{x}u

6.D_{x}\csc^{-1}{u} = -\frac{1}{u\sqrt{u^{2}-1}}D_{x}u


Derivative involving hyperbolic trigonometric functions

Hyperbolic trigonometric functions

1.D_{x}\sinh(u) = \cosh(u)D_{x}u

2.D_{x}\cosh(u) = \sinh(u)D_{x}u

3.D_{x}\tanh(u) = sech^{2}(u)D_{x}u

4.D_{x}\coth(u) = -csch^{2}(u)D_{x}u

5.D_{x}sech(u) = -sech(u)tanh(u)D_{x}u

6.D_{x}csch(u) = -csch(u)\coth(u)D_{x}u


NEXT TABLE: Table of integrals