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Differential Calculus

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Question : 22 of 69

Marks: +1, -0

If

f(x)=e^{5 x}+e^{-5 x}

f'(x)

is

$5 f(x)$
$f(x)$
$25 f(x)$
none

Solution:

Concept:

Derivative of exponential functions:

\frac{d}{dx} e^{kx} = k e^{kx}

.

Explanation:

Given

f(x)=e^{5x}+e^{-5x}

.

Differentiate term by term:

f'(x)=5e^{5x} + (-5)e^{-5x} = 5e^{5x} - 5e^{-5x}

.

Factor out 5:

f'(x)=5(e^{5x}-e^{-5x})

.

This is not equal to

5f(x)

(which would be

5e^{5x}+5e^{-5x}

), nor to

f(x)

, nor to

25f(x)

.

Answer:

Hence, the correct option is D. none.

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