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Popular >

derivative of (3x^2+5)e^{4x}

Solution

derivative of

(3 x^{2} + 5) e^{4 x}

Solution

6 x e^{4 x} + e^{4 x} \cdot 4 (3 x^{2} + 5)

Solution steps

\frac{d}{d x} ((3 x^{2} + 5) e^{4 x})

Apply the Product Rule:

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

f = 3 x^{2} + 5, g = e^{4 x}

= \frac{d}{d x} (3 x^{2} + 5) e^{4 x} + \frac{d}{d x} (e^{4 x}) (3 x^{2} + 5)

\frac{d}{d x} (3 x^{2} + 5) = 6 x

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

= 6 x e^{4 x} + e^{4 x} \cdot 4 (3 x^{2} + 5)

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^2+5)e^{4x} ?
The derivative of (3x^2+5)e^{4x} is 6xe^{4x}+e^{4x}*4(3x^2+5)
What is the first derivative of (3x^2+5)e^{4x} ?
The first derivative of (3x^2+5)e^{4x} is 6xe^{4x}+e^{4x}*4(3x^2+5)