What is the derivative of e^{3x}+3xe^{3x} ?

The derivative of e^{3x}+3xe^{3x} is 6e^{3x}+9e^{3x}x

What is the first derivative of e^{3x}+3xe^{3x} ?

The first derivative of e^{3x}+3xe^{3x} is 6e^{3x}+9e^{3x}x

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Popular >

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

6 e^{3 x} + 9 e^{3 x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{3 x} \cdot 3 + 3 (e^{3 x} + 3 e^{3 x} x)

Simplify

e^{3 x} \cdot 3 + 3 (e^{3 x} + 3 e^{3 x} x) : 6 e^{3 x} + 9 e^{3 x} x

= 6 e^{3 x} + 9 e^{3 x} x

\frac{d}{d x} (2 x^{4 + 7 x + 5})

\int \frac{y}{( 1 + y ^{2} )} d y

\int \frac{4 x ^{2} - 3 x + 4}{x ^{3} + 4 x} d x

y^{^{''}} + 2 y^{^{'}} + y = 2 e^{- x}

\frac{d}{d x} (36 x^{2} - 72 x)

What is the derivative of e^{3x}+3xe^{3x} ?
The derivative of e^{3x}+3xe^{3x} is 6e^{3x}+9e^{3x}x
What is the first derivative of e^{3x}+3xe^{3x} ?
The first derivative of e^{3x}+3xe^{3x} is 6e^{3x}+9e^{3x}x