What is the derivative of 4xe^{4x} ?

The derivative of 4xe^{4x} is 4(e^{4x}+4e^{4x}x)

What is the first derivative of 4xe^{4x} ?

The first derivative of 4xe^{4x} is 4(e^{4x}+4e^{4x}x)

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

4 (e^{4 x} + 4 e^{4 x} x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 4 (1 \cdot e^{4 x} + e^{4 x} \cdot 4 x)

Simplify

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

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