Derivative Calculator

Calculate derivatives of mathematical functions instantly. Enter any function and get the derivative with step-by-step explanations.

Function Input
Enter a mathematical function (e.g., x^2 + 3*x + 1, sin(x), e^x)
basic Functions
Click any example to try it in the calculator

Linear Function

basic
Function:
f(x) = 3*x + 2
Derivative:
f'(x) = 3

Simple linear function with constant derivative

Quadratic

basic
Function:
f(x) = x^2
Derivative:
f'(x) = 2*x

Basic quadratic using power rule

Cubic Polynomial

basic
Function:
f(x) = x^3 - 2*x^2 + x - 1
Derivative:
f'(x) = 3*x^2 - 4*x + 1

Multi-term polynomial

Power Function

basic
Function:
f(x) = x^5
Derivative:
f'(x) = 5*x^4

Higher-order power function

trigonometric Functions
Click any example to try it in the calculator

Sine Function

trigonometric
Function:
f(x) = sin(x)
Derivative:
f'(x) = cos(x)

Basic trigonometric derivative

Cosine Function

trigonometric
Function:
f(x) = cos(x)
Derivative:
f'(x) = -sin(x)

Cosine derivative with negative

Tangent Function

trigonometric
Function:
f(x) = tan(x)
Derivative:
f'(x) = sec^2(x)

Tangent derivative using secant

Sine Composition

trigonometric
Function:
f(x) = sin(2*x)
Derivative:
f'(x) = 2*cos(2*x)

Chain rule with trigonometric function

exponential Functions
Click any example to try it in the calculator

Natural Exponential

exponential
Function:
f(x) = exp(x)
Derivative:
f'(x) = exp(x)

e^x derivative equals itself

Base-2 Exponential

exponential
Function:
f(x) = 2^x
Derivative:
f'(x) = 2^x * ln(2)

Exponential with different base

Natural Logarithm

exponential
Function:
f(x) = ln(x)
Derivative:
f'(x) = 1/x

Natural log derivative

Exponential Chain

exponential
Function:
f(x) = exp(x^2)
Derivative:
f'(x) = 2*x*exp(x^2)

Chain rule with exponential

advanced Functions
Click any example to try it in the calculator

Product Rule

advanced
Function:
f(x) = x * sin(x)
Derivative:
f'(x) = sin(x) + x*cos(x)

Product of polynomial and trigonometric

Quotient Rule

advanced
Function:
f(x) = sin(x) / x
Derivative:
f'(x) = (x*cos(x) - sin(x)) / x^2

Division of functions

Chain Rule Complex

advanced
Function:
f(x) = sqrt(1 + x^2)
Derivative:
f'(x) = x / sqrt(1 + x^2)

Square root with chain rule

Mixed Functions

advanced
Function:
f(x) = x^2 * exp(x) + sin(x)
Derivative:
f'(x) = 2*x*exp(x) + x^2*exp(x) + cos(x)

Combination of multiple rules