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Popular >

derivative of ax^2e^{4x}

Solution

\frac{d}{d x} (a x^{2} e^{4 x})

Solution

a (2 x e^{4 x} + e^{4 x} \cdot 4 x^{2})

Solution steps

\frac{d}{d x} (a x^{2} e^{4 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (x^{2} e^{4 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{4 x}

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

\frac{d}{d x} (x^{2}) = 2 x

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

= a (2 x e^{4 x} + e^{4 x} \cdot 4 x^{2})

Graph

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integral of x/(sqrt(27+x^2))

\int \frac{x}{27 + x ^{2}} d x

\frac{d}{d t} (2 t e^{t})

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\frac{d}{d x} (x (x + 1)^{2})

Frequently Asked Questions (FAQ)

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