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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