What is the derivative of 2xe^{3x}+e^{3x}*3x^2 ?

The derivative of 2xe^{3x}+e^{3x}*3x^2 is 9e^{3x}x^2+12e^{3x}x+2e^{3x}

What is the first derivative of 2xe^{3x}+e^{3x}*3x^2 ?

The first derivative of 2xe^{3x}+e^{3x}*3x^2 is 9e^{3x}x^2+12e^{3x}x+2e^{3x}

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

9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 (e^{3 x} + 3 e^{3 x} x) + 3 (e^{3 x} \cdot 3 x^{2} + 2 x e^{3 x}) : 9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x}

= 9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x}

\frac{\partial}{\partial x} (3 cos (3 x))

x \to 0 lim (\frac{2 x - x}{x})

\int \frac{x + 5}{x ^{2} + 5 x + 6} d x

y = x^{2} - 9, y = 8 x

e^{2 t} sin (j) (2 t)

What is the derivative of 2xe^{3x}+e^{3x}*3x^2 ?
The derivative of 2xe^{3x}+e^{3x}*3x^2 is 9e^{3x}x^2+12e^{3x}x+2e^{3x}
What is the first derivative of 2xe^{3x}+e^{3x}*3x^2 ?
The first derivative of 2xe^{3x}+e^{3x}*3x^2 is 9e^{3x}x^2+12e^{3x}x+2e^{3x}