Derivative Calculator

Compute derivatives with step-by-step solutions using calculus differentiation rules.

Enter Expression
d/dx
Variable: Order:
Steps: Full working
Try these examples
$x^3 + 2*x^2 - 5$$sin(x)*cos(x)$$ln(x^2 + 1)$$x^2*exp(-x)$$arctan(x)$$(x^2 + 1)/(x - 1)$$sqrt(x^2 + 4)$$x*ln(x)$$sin(x^2)$$cos(x)/x$$tan(x)^2$$exp(sin(x))$
Steps Modes
None  Show answer only — clean output.
Summary  Pill list of every rule used.
Detailed  Accordion with before → after expressions, formula, and plain-language explanation per step.
Tip: In Detailed mode, click any step header to expand/collapse it.
Differentiation Rules
Constant$d/dx[c]=0$
Power$d/dx[x^n]=nx^{n-1}$
Sum$d/dx[f±g]=f'±g'$
Product$d/dx[fg]=f'g+fg'$
Quotient$d/dx[f/g]=(f'g-fg')/g²$
Chain$d/dx[f(g)]=f'(g)·g'$
sin(x)$cos(x)$
cos(x)$−sin(x)$
tan(x)$sec²(x)$
ln(x)$1/x$
eˣ$eˣ$
arctan(x)$1/(1+x²)$
Supported Functions
sin()cos()tan()cot()sec()csc()arcsin()arccos()arctan()sinh()cosh()tanh()ln()log()sqrt()exp()abs()
Use ^ for powers, * for multiplication.
Input Tips
  • x^2 → x²
  • sin(x) → trig
  • ln(x) → natural log
  • sqrt(x) → √x
  • exp(x) → eˣ
  • 2.71828 → e
  • 3.14159 → π
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