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Chain Rule, Log Differentiation & Rate of Change · Question 65 of 130

Question 65

MediumOriginal question

If f(x)=e3xcos⁡xf(x) = e^{3 x} \cos x, what is f′(0)f'\left(0\right)?

Options for question 65

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. f′(x)=3e3xcos⁡x−e3xsin⁡xf'(x) = 3e^{3x}\cos x - e^{3x}\sin x.

  2. At 0: 3−0=33 - 0 = 3.

Worth noting

1 differentiates e3xe^{3x} as e3xe^{3x}, forgetting the 3.

Concept
A product with an exponential, at a point
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.