1. Formula
- `d/(dx)(c)=0`
- `d/(dx)(x)=1`
- `d/(dx)(x^n)=n * x^(n-1)`
- `d/(dx)(u+v)=(du)/(dx)+(dv)/(dx)`
- `d/(dx)(cu)=c(du)/(dx)`
- `d/(dx)(uv)=u(dv)/(dx)+v(du)/(dx)`
- `d/(dx)(u/v)=(v(du)/(dx)-u(dv)/(dx))/(v^2)`
Derivative of Trigonometric Functions
- `d/(dx)(e^x)=e^x`
- `d/(dx)(a^x)=a^x` `log_(e)a`
- `d/(dx)(log(x))=1/x`
- `d/(dx)(sin(x))=cos(x)`
- `d/(dx)(cos(x))=-sin(x)`
- `d/(dx)(tan(x))=sec^2(x)`
- `d/(dx)(cosec(x))=-cosec(x) * cot(x)`
- `d/(dx)(sec(x))=sec(x) * tan(x)`
- `d/(dx)(cot(x))=-cosec^2(x)`
- `d/(dx)(sin^-1(x))=1/(sqrt(1-x^2))`
- `d/(dx)(cos^-1(x))=(-1)/(sqrt(1-x^2))`
- `d/(dx)(tan^-1(x))=1/(1+x^2)`
- `d/(dx)(cosec^-1(x))=(-1)/(1+x^2)`
- `d/(dx)(sec^-1(x))=1/(|x|sqrt(x^2-1))`
- `d/(dx)(cot^-1(x))=(-1)/(|x|sqrt(x^2-1))`
- `d/(dx)(sqrt(x))=1/(2sqrt(x))`
- `d/(dx)(1/x)=(-1)/x^2`
Derivative of the Hyperbolic functions
- `d/(dx)(sinh(x))=cosh(x)`
- `d/(dx)(cosh(x))=sinh(x)`
- `d/(dx)(tanh(x))=sec^2h(x)`
- `d/(dx)(cosech(x))=-cosech(x) * coth(x)`
- `d/(dx)(sech(x))=-sech(x) * tanh(x)`
- `d/(dx)(coth(x))=-cosec^2h(x)`
This material is intended as a summary. Use your textbook for detail explanation.
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