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Popular Calculus >

derivative of 16e^{2x}x+32e^{2x}

Solution

\frac{d}{d x} (16 e^{2 x} x + 32 e^{2 x})

Solution

32 e^{2 x} x + 80 e^{2 x}

Solution steps

\frac{d}{d x} (16 e^{2 x} x + 32 e^{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (16 e^{2 x} x) + \frac{d}{d x} (32 e^{2 x})

\frac{d}{d x} (16 e^{2 x} x) = 16 (2 e^{2 x} x + e^{2 x})

\frac{d}{d x} (32 e^{2 x}) = 64 e^{2 x}

= 16 (2 e^{2 x} x + e^{2 x}) + 64 e^{2 x}

Simplify

16 (2 e^{2 x} x + e^{2 x}) + 64 e^{2 x} : 32 e^{2 x} x + 80 e^{2 x}

= 32 e^{2 x} x + 80 e^{2 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 16e^{2x}x+32e^{2x} ?
The derivative of 16e^{2x}x+32e^{2x} is 32e^{2x}x+80e^{2x}
What is the first derivative of 16e^{2x}x+32e^{2x} ?
The first derivative of 16e^{2x}x+32e^{2x} is 32e^{2x}x+80e^{2x}