Derivative calculator with steps

What this page covers

• Derivatives of polynomials, powers, exponentials, logarithms and trigonometric functions.
• The product, quotient and chain rules, applied one step at a time.
• Higher derivatives when you ask for them (write d²/dx²).
• Not covered here: integrals (use Integral calculator with steps), and implicit or partial derivatives beyond the basic cases, which you can still type and try.

How to enter the problem

• Type it as d/dx followed by the function in brackets, or use the math keyboard's derivative key.
• Scan it. Fit the one expression in the frame.
• Choose a photo. Several problems in one photo are solved as a list.
• Then tap Solve.

Worked example

Common mistakes

• Forgetting the inner derivative in the chain rule, which gives $e^{2x}(\cos 3x - \sin 3x)$ instead of the correct answer.
• Differentiating a product factor by factor, as if $(uv)'$ were $u'v'$.
• Losing the sign of the derivative of cosine: $(\cos 3x)' = -3\sin 3x$.
• Treating $\ln x$ as a constant in expressions like $x^2 \ln x$; its derivative is $1/x$.

Checks, assumptions and limits

• Check numerically. Pick a point, say $x = 1$. The formula gives about $-17.758$. Estimate the slope from the original function with a tiny step, for example $[f(1.000001) - f(0.999999)] / 0.000002$, and compare.
• Angles are in radians. In degrees the chain rule adds a factor of $\pi/180$.
• Domain matters for logarithms and roots: $x^2 \ln x$ and its derivative exist only for $x > 0$.
• HexMath can make mistakes. Double check important steps.

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