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 | ||||
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Derivative of ordinary exponential and logarithmic functions
Simple Logarithmic and Exponential Functions | |||
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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 |
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