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Popular >

derivative of (4x-8e^{4x})

Solution

\frac{d}{d x} ((4 x - 8) e^{4 x})

Solution

16 e^{4 x} x - 28 e^{4 x}

Solution steps

\frac{d}{d x} ((4 x - 8) e^{4 x})

Apply the Product Rule:

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

f = 4 x - 8, g = e^{4 x}

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

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 4 e^{4 x} + e^{4 x} \cdot 4 (4 x - 8)

Simplify

4 e^{4 x} + e^{4 x} \cdot 4 (4 x - 8) : 16 e^{4 x} x - 28 e^{4 x}

= 16 e^{4 x} x - 28 e^{4 x}

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Frequently Asked Questions (FAQ)

What is the derivative of (4x-8e^{4x}) ?
The derivative of (4x-8e^{4x}) is 16e^{4x}x-28e^{4x}
What is the first derivative of (4x-8e^{4x}) ?
The first derivative of (4x-8e^{4x}) is 16e^{4x}x-28e^{4x}