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Chain Rule, Log Differentiation & Rate of Change · Question 74 of 130

Question 74

MediumOriginal question

What is ddx(ex(sin⁡x+cos⁡x))\frac{d}{dx}\left(e^{x}(\sin x + \cos x)\right)?

Options for question 74

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Product rule: ex(sin⁡x+cos⁡x)+ex(cos⁡x−sin⁡x)e^{x}(\sin x + \cos x) + e^{x}(\cos x - \sin x).

  2. The sin⁡x\sin x terms cancel: 2excos⁡x2e^{x}\cos x.

Worth noting

ex(cos⁡x−sin⁡x)e^{x}(\cos x - \sin x) differentiates only the bracket and drops the term from (ex)′=ex(e^{x})' = e^{x}.

Concept
Exponential and logarithm inside a chain
Typical time
90 s
Your time
—
The rule this testsExponential and logarithmic functions
Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.