# Derivative Calculator

## What Is Derivative?

In mathematics, the “derivative” measures the sensitivity to change of output value with respect to a change in the input value but in calculus, derivatives are central tools.

Did You Know!

Many statisticians have defined derivatives simply by the following formula:

• d/dxf=f(x)=limh0f(x+h)f(x)/h

Check More

Percentage Calculator

Common Functions Function Derivative
Constant c 0
Line x 1
ax a
Square x2 2x
Square Root √x (½)x
Exponential ex ex
ax ln(a) ax
Logarithms ln(x) 1/x
loga(x) 1 / (x ln(a))
Trigonometry (x is in radians) sin(x) cos(x)
cos(x) −sin(x)
tan(x) sec2(x)
Inverse Trigonometry sin-1(x) 1/√(1−x2)
cos-1(x) −1/√(1−x2)
tan-1(x) 1/(1+x2)

Derivative Calculator

Rules Function Derivative
Multiplication by constant cf cf’
Power Rule xn nxn−1
Sum Rule f + g f’ + g’
Difference Rule f – g f’ − g’
Product Rule fg f g’ + f’ g
Quotient Rule f/g (f’ g − g’ f )/g2
Reciprocal Rule 1/f −f’/f2
Chain Rule
(as “Composition of Functions”)
f º g (f’ º g) × g’
Chain Rule
(using ’ )
f(g(x)) f’(g(x))g’(x)
Chain Rule
(using dydxdydx)
dydx=dydududxdydx=dydududx