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Popular Calculus >

derivative of (4+8xcos(1-x))

Solution

\frac{d}{d x} ((4 + 8 x) cos (1 - x))

Solution

8 cos (1 - x) + sin (1 - x) (4 + 8 x)

Solution steps

\frac{d}{d x} ((4 + 8 x) cos (1 - x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 + 8 x, g = cos (1 - x)

= \frac{d}{d x} (4 + 8 x) cos (1 - x) + \frac{d}{d x} (cos (1 - x)) (4 + 8 x)

\frac{d}{d x} (4 + 8 x) = 8

\frac{d}{d x} (cos (1 - x)) = sin (1 - x)

= 8 cos (1 - x) + sin (1 - x) (4 + 8 x)

Graph

Popular Examples

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\frac{d}{d x} ((x + 1) (x^{3} + 3))

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\int \frac{4 x + 1}{2 x ^{2} + x - 3} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (4+8xcos(1-x)) ?
The derivative of (4+8xcos(1-x)) is 8cos(1-x)+sin(1-x)(4+8x)
What is the first derivative of (4+8xcos(1-x)) ?
The first derivative of (4+8xcos(1-x)) is 8cos(1-x)+sin(1-x)(4+8x)