Derivatives and integrals practice problems with worked answers

You do the maths yourself and type your answer, like on a calculator. Every equivalent form counts. Five problems, new every day, with worked solutions and the typical mistake. Free and without an account.

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The basics without a daily limit in a free account, plus one exam-level task a day. Every level, the exam mode and the AI tutor from €4.99 once or with Plus.

Task 1 of 5e^x, ln, sin, cos

Task

Differentiate:

f (x) = 4 e^{x} + 5 ln (x) + 2 sin (x)

$f^{'} (x) =$

Write like on a calculator: 3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x). Use brackets: e^(2x), not e^2x. Numbers also as 3/4 or e^2 - 1.

Topics with rules and practicePower and sum rule · e^x, ln, sin, cos · Antiderivatives · Definite integrals …

Power and sum rule e^x, ln, sin, cos Antiderivatives Definite integrals Product rule Quotient rule Chain rule Tangent line Maxima and minima Integration by substitution Integration by parts Limits and L’Hôpital

How the trainer works

Type it like on a calculator

3x^2 - 2/x, e^(2x), sqrt(x), ln(x), sin(x): the input understands the usual notation, even without multiplication signs.

Every correct form counts

Factored or expanded: the trainer compares your function with the solution at many points. For antiderivatives the + C does not matter.

Always new problems

Every problem is generated with new numbers, without AI and always computed correctly. You practise the rule, not memorising answers.