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Popular >

derivative of 4e^{3x}+12xe^{3x}

Solution

\frac{d}{d x} (4 e^{3 x} + 12 x e^{3 x})

Solution

24 e^{3 x} + 36 e^{3 x} x

Solution steps

\frac{d}{d x} (4 e^{3 x} + 12 x e^{3 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 e^{3 x}) + \frac{d}{d x} (12 x e^{3 x})

\frac{d}{d x} (4 e^{3 x}) = 12 e^{3 x}

\frac{d}{d x} (12 x e^{3 x}) = 12 (e^{3 x} + 3 e^{3 x} x)

= 12 e^{3 x} + 12 (e^{3 x} + 3 e^{3 x} x)

Simplify

12 e^{3 x} + 12 (e^{3 x} + 3 e^{3 x} x) : 24 e^{3 x} + 36 e^{3 x} x

= 24 e^{3 x} + 36 e^{3 x} x

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Frequently Asked Questions (FAQ)

What is the derivative of 4e^{3x}+12xe^{3x} ?
The derivative of 4e^{3x}+12xe^{3x} is 24e^{3x}+36e^{3x}x
What is the first derivative of 4e^{3x}+12xe^{3x} ?
The first derivative of 4e^{3x}+12xe^{3x} is 24e^{3x}+36e^{3x}x