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Popular Calculus >

derivative of (4+8xcosh(2x))

Solution

\frac{d}{d x} ((4 + 8 x) cosh (2 x))

Solution

8 cosh (2 x) + sinh (2 x) \cdot 2 (4 + 8 x)

Solution steps

\frac{d}{d x} ((4 + 8 x) cosh (2 x))

Apply the Product Rule:

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

f = 4 + 8 x, g = cosh (2 x)

= \frac{d}{d x} (4 + 8 x) cosh (2 x) + \frac{d}{d x} (cosh (2 x)) (4 + 8 x)

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

\frac{d}{d x} (cosh (2 x)) = sinh (2 x) \cdot 2

= 8 cosh (2 x) + sinh (2 x) \cdot 2 (4 + 8 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (4+8xcosh(2x)) ?
The derivative of (4+8xcosh(2x)) is 8cosh(2x)+sinh(2x)*2(4+8x)
What is the first derivative of (4+8xcosh(2x)) ?
The first derivative of (4+8xcosh(2x)) is 8cosh(2x)+sinh(2x)*2(4+8x)