How to use it
- Type the function, for example x^3 * sin(x) or 3x^2 + 2x. Use ^ for powers, ln(x) for the natural log and exp(x) or e^x for the exponential.
- Choose the variable (x by default) and the order: 1 for the first derivative, 2 for the second, and so on.
- Optionally enter a value to evaluate the derivative at that point, for example the slope of the tangent line.
Rules the calculator applies
Power rule: d/dx xⁿ = n·xⁿ⁻¹. Sum rule: differentiate term by term.
Product rule: (uv)′ = u′v + uv′. Quotient rule: (u/v)′ = (u′v − uv′) / v². Chain rule: f(g(x))′ = f′(g(x))·g′(x).
Standard derivatives: (sin x)′ = cos x, (cos x)′ = −sin x, (eˣ)′ = eˣ, (ln x)′ = 1/x.
Example
For f(x) = x³ sin(x), the product rule gives f′(x) = 3x² sin(x) + x³ cos(x). At x = 0, the derivative is 0.
Radians in calculus
Derivative formulas for trig functions assume radians. The calculator always uses radians here, even if the main calculator is set to degrees.
Frequently asked questions
Can it find second and higher derivatives?
Yes. Set the order to any number from 1 to 8.
How do I write the natural log?
Type ln(x). log(x) means the base-10 logarithm.
Can I differentiate with respect to a variable other than x?
Yes. Type the variable name, such as t, in the Variable box and use it in the function.
Does it show the slope at a point?
Enter a value in "Evaluate at". The result is the slope of the tangent line at that point.