Derivative Calculator

Derivative Calculator

Calculate derivatives with step-by-step explanations

Enter Function f(x)

Differentiation Variable

Try an example:

DERIVATIVE

Step-by-Step Solution

Calculation History

Derivative Rules & Functions

Constant Rule

d(c)/dx = 0

Power Rule

d(xⁿ)/dx = n·xⁿ⁻¹

Sum Rule

(f + g)' = f' + g'

Product Rule

(fg)' = f'g + fg'

Quotient Rule

(f/g)' = (f'g − fg')/g²

Chain Rule

f(g(x))' = f'(g(x))g'(x)

Sine

d(sin x)/dx = cos x

Cosine

d(cos x)/dx = −sin x

Tangent

d(tan x)/dx = sec²x

Natural Logarithm

d(ln x)/dx = 1/x

Exponential

d(eˣ)/dx = eˣ

Square Root

d(√x)/dx = 1/(2√x)

Supported Functions

You can enter mathematical expressions using the following functions and operators.

Basic Operators

+   −   *   /   ^

Trigonometric

sin(x), cos(x), tan(x)

Logarithmic

ln(x), log(x)

Exponential

e^x, exp(x)

Roots

sqrt(x)

Constants

pi, e

Frequently Asked Questions

What is a derivative?

A derivative measures how quickly a function changes with respect to its variable. Geometrically, it represents the slope of the tangent line to a curve.

How do I enter multiplication?

Use the asterisk (*) symbol. For example, enter 3*x^2 instead of 3x^2.

How do I enter powers?

Use the caret symbol (^). For example, x^3 means x raised to the third power.

Can I calculate trigonometric derivatives?

Yes. The calculator supports functions such as sin(x), cos(x), and tan(x), including expressions involving them.

Can I differentiate a product?

Yes. For example, you can enter x^2*sin(x). The calculator applies symbolic differentiation to the expression.

Is my calculation history saved?

Recent calculations are stored locally in your browser using localStorage. They are not sent to a server by this calculator.

Is this derivative calculator free?

Yes. This calculator can be embedded on a blog and used without creating an account.