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Popular >

derivative of e^{4x}+4e^{4x}x

Solution

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

Solution

16 e^{4 x} x + 8 e^{4 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

= 16 e^{4 x} x + 8 e^{4 x}

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Frequently Asked Questions (FAQ)

What is the derivative of e^{4x}+4e^{4x}x ?
The derivative of e^{4x}+4e^{4x}x is 16e^{4x}x+8e^{4x}
What is the first derivative of e^{4x}+4e^{4x}x ?
The first derivative of e^{4x}+4e^{4x}x is 16e^{4x}x+8e^{4x}