Derivative Calculator
Enter any expression and get a full step-by-step solution — free, instantly.
Differentiation Rules Supported
Power Rule
d/dx[xⁿ] = n·xⁿ⁻¹
Sum / Difference Rule
(f ± g)' = f' ± g'
Constant Multiple Rule
(c·f)' = c·f'
Product Rule
(f·g)' = f'g + fg'
Quotient Rule
(f/g)' = (f'g − fg')/g²
Chain Rule
f(g(x))' = f'(g(x))·g'(x)
Exponential (eˣ)
d/dx[eˣ] = eˣ
Natural Log
d/dx[ln x] = 1/x
Trig Functions
sin, cos, tan and their inverses
Square Root
d/dx[√x] = 1/(2√x)
Hyperbolic Functions
sinh, cosh, tanh and their inverses
How to Use
- Type your expression using standard math notation (e.g.
x^2 * sin(x)or2x·sin(x)). - Use
^for exponents,*for multiplication (or write terms together —2xis understood), and/for division. - Trig:
sin,cos,tan,asin,acos,atan. Hyperbolic:sinh,cosh,tanh,asinh,acosh,atanh. Other:ln,exp,sqrt. - Select the variable you want to differentiate with respect to (default: x).
- Press Calculate Derivative or hit Enter.
Common Derivatives
| f(x) | f′(x) |
|---|---|
| xⁿ | n·xⁿ⁻¹ |
| eˣ | eˣ |
| ln(x) | 1/x |
| sin(x) | cos(x) |
| cos(x) | −sin(x) |
| tan(x) | sec²(x) |
| arcsin(x) | 1/√(1−x²) |
| arccos(x) | −1/√(1−x²) |
| arctan(x) | 1/(1+x²) |
| √x | 1/(2√x) |
| sinh(x) | cosh(x) |
| cosh(x) | sinh(x) |
| tanh(x) | sech²(x) |
| arcsinh(x) | 1/√(1+x²) |
| arctanh(x) | 1/(1−x²) |