Verified Calculus Solver with Step-by-Step Explanations

Derivative Calculator with Steps

Differentiate first-order, higher-order and common multivariable expressions while seeing the exact rule used at each step.

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Dedicated workspace

Derivative solver

Engine

Use ^ for powers and parentheses for functions. You can enter sec(x) and arctan(x) directly; trigonometric inputs use radians.

Input help and supported methods

Keep the original question visible. Confirm the variable and the live preview before calculating. Use ^(1/2) for a square root and explicit parentheses for function arguments.

Choose the differentiation variable and order. Symbols other than the selected variable are constants. For an equation containing y, use implicit differentiation.

Read the method

Try an example

Live problem preview

Choose the right workflow

Which derivative task do you have?

Start with the structure of the problem. Each option keeps its own notation, variables and deterministic steps.

DerivativesDifferentiate a single-variable expression or compute a higher-order derivative.
ddx[x3+2 x]\frac{\mathrm{d}}{\mathrm{d}x}\left[x^{3} + 2\,x\right]
Use the calculator above
Chain rule calculatorDifferentiate a composite function by identifying and multiplying its outer and inner rates.
ddx[(x2+1)3]\frac{\mathrm{d}}{\mathrm{d}x}\left[\left(x^{2} + 1\right)^{3}\right]
Open this calculatorPartial derivative calculatorChoose one independent variable and hold the others constant.
∂∂x[x2 y+y3]\frac{\partial}{\partial x}\left[x^{2}\,y + y^{3}\right]
Open this calculatorImplicit differentiationDifferentiate an equation that links x and y while treating y as a function of x.
x2+y2=25x^{2} + y^{2} = 25
Open this calculator

Function derivative formulas

Derivative of ln(x) (English guide)Derivative of arctan(x) (English guide)Derivative of tan(x) (English guide)Derivative of sec(x) (English guide)

Differentiation methods

How to Find Partial Derivatives (English guide)How to Use the Chain Rule (English guide)How to Do Implicit Differentiation (English guide)

Rules you can recognize

How this calculator chooses a method

Power and sum rules

ddxxn=nxn−1\frac{\mathrm{d}}{\mathrm{d}x}x^n=nx^{n-1}

Differentiate each term separately, bring constant exponents forward, and preserve constants and signs through the sum.

Product and quotient rules

(uv)′=u′v+uv′(uv)^{\prime}=u^{\prime}v+uv^{\prime}

Split an expression into factors or a numerator and denominator, then account for the derivative of every changing part.

Chain rule

(f∘g)′=f′(g) g′(f\circ g)^{\prime}=f^{\prime}(g)\,g^{\prime}

Recognize nested functions, differentiate the outer function first, and multiply by the derivative of the inner function.

Three clear moves

How to use this calculator

Choose the differentiation variable and an order from one to five. The engine builds a symbolic rule tree, simplifies the result, and independently recomputes first derivatives before marking them Verified.

Enter one expression using standard mathematical syntax.

Choose the variable and task-specific options.

Review the result, verification note and ordered steps.

Verified means checked, not merely generated

Continue with a related calculator built for a different calculus intent.

partial derivative calculatorChoose one independent variable and hold the others constant.Chain rule calculatorDifferentiate a composite function by identifying and multiplying its outer and inner rates.Implicit differentiationDifferentiate an equation that links x and y while treating y as a function of x.IntegralsFind an antiderivative for an expression without finite bounds.LimitsEvaluate finite, infinite, or one-sided behavior near an approach value.