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Differential Calculus

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Question : 2 of 69

Marks: +1, -0

If

f(x)=(2 x^{2}+5 x-3)(4 x+1)

f'(x)

is

$24 x^{2}+44 x+7$
$24 x^{2}+44 x-7$
$8 x^{2}+22 x-7$
none

Solution:

Concept:

Use the product rule of differentiation:

(uv)' = u'v + uv'

.

Explanation:

Let

u = 2x^2 + 5x - 3

and

v = 4x + 1

.

Then

u' = 4x + 5

and

v' = 4

.

Apply product rule:

f'(x) = u'v + uv' = (4x + 5)(4x + 1) + (2x^2 + 5x - 3) \cdot 4

.

Compute first part:

(4x + 5)(4x + 1) = 16x^2 + 4x + 20x + 5 = 16x^2 + 24x + 5

.

Compute second part:

(2x^2 + 5x - 3) \cdot 4 = 8x^2 + 20x - 12

.

Add them:

(16x^2 + 24x + 5) + (8x^2 + 20x - 12) = 24x^2 + 44x - 7

.

Answer:

f'(x) = 24x^2 + 44x - 7

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