Derivative of product rule or differentiation of product rule
let f(x)=u.v
where u and v are function of x
\frac d{dx}f\left(x\right)=\frac d{dx}\left[\left(u\right).\left(v\right)\right] \boxed{\frac d{dx}f\left(x\right)=\left(u\right).\frac d{dx}\left(v\right)+\left(v\right).\frac d{dx}\left(u\right)}Derivative of quotient rule or differentiation of quotient rule
f\left(x\right)=\frac uvwhere u and v are function of x
\frac d{dx}f\left(x\right)=\frac d{dx}\frac uv \boxed{\frac d{dx}f\left(x\right)=\frac{\left(v\right).{\displaystyle\frac d{dx}}\left(u\right)-\left(u\right).{\displaystyle\frac d{dx}}\left(v\right)}{\left(v\right)^2}}Derivative of power rule or differentiation of power rule
f\left(x\right)=x^n \frac d{dx}f\left(x\right)=\frac d{dx}x^n \boxed{\frac d{dx}f\left(x\right)=nx^{n-1}}Derivative of chain rule or differentiation of chain rule
Let y=f(u) and u=g(x)
\boxed{\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}}Derivative of trigonometric functions or Differentiation of trigonometric functions
\boxed{\frac d{dx}\left(\sin x\right)=\cos x} \boxed{\frac d{dx}\left(\cos x\right)=-sin x} \boxed{\frac d{dx}\left(\tan x\right)=sec^2 x} \boxed{\frac d{dx}\left(\cot x\right)=-cosec^2 x} \boxed{\frac d{dx}\left(\cosec x\right)=-cosec x.cot x} \boxed{\frac d{dx}\left(\sec x\right)=sec x.tan x}Derivative of inverse trigonometric functions ,Differentiation of inverse trigonometric functions
\boxed{\frac d{dx}(Sin^{-1}x)=\frac1{\sqrt{1-x^2}}} \boxed{\frac d{dx}(Cos^{-1}x)=\frac{-1}{\sqrt{1-x^2}}} \boxed{\frac d{dx}(Tan^{-1}x)=\frac{1}{{1+x^2}}} \boxed{\frac d{dx}(Cot^{-1}x)=\frac{-1}{{1+x^2}}} \boxed{\frac d{dx}(sec^{-1}x)=\frac1{\left|x\right|\sqrt{1-x^2}}} \boxed{\frac d{dx}(Cosec^{-1}x)=\frac{-1}{\left|x\right|\sqrt{1-x^2}}}Derivative of sum and difference rule, Differentiation of sum and difference rule
sum rule of Derivative
let y=u(x)+v(x)
where u and v are function of x
\boxed{\frac d{dx}\left(y\right)=\frac d{dx}\left[u\left(x\right)+v\left(x\right)\right]}difference rule of Derivative
let y=u(x)-v(x)
where u and v are function of x
\boxed{\frac d{dx}\left(y\right)=\frac d{dx}\left[u\left(x\right)-v\left(x\right)\right]}Derivative of hyperbolic functions
\boxed{Sinhx=\frac{e^x-e^{-x}}2}
\boxed{Coshx=\frac{e^x+e^{-x}}2}
\boxed{Tanhx=\frac{Sinhx}{Coshx}=\frac{e^x+e^{-x}}{e^x-e^{-x}}}
\boxed{Cosechx=\frac1{Sinhx}=\frac2{e^x-e^{-x}}}
\boxed{Sechx=\frac1{Coshx}=\frac2{e^x+e^{-x}}}
\boxed{Cothx=\frac{Coshx}{Sinhx}=\frac{e^x+e^{-x}}{e^x-e^{-x}}}
Logarithmic differentiation
\boxed{\frac d{dx}\ln x=\frac1x}
Derivative of constant is zero
\boxed{\frac{dy}{dx}=0}