What is the derivative of x^2e^{7x} ?

The derivative of x^2e^{7x} is 2xe^{7x}+e^{7x}*7x^2

What is the first derivative of x^2e^{7x} ?

The first derivative of x^2e^{7x} is 2xe^{7x}+e^{7x}*7x^2

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\frac{d}{d x} (x^{2} e^{7 x})

2 x e^{7 x} + e^{7 x} \cdot 7 x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{7 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{7 x}

= \frac{d}{d x} (x^{2}) e^{7 x} + \frac{d}{d x} (e^{7 x}) x^{2}

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

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= 2 x e^{7 x} + e^{7 x} \cdot 7 x^{2}

\int \frac{( e ^{t} + 2 e ^{2 t} )}{e ^{3 t}} d t

\frac{\partial}{\partial x} (\frac{u}{x})

\int_{- 1}^{1} 2 1 - \frac{x ^{2}}{2} d x

\frac{12 x}{x ^{6}}

x \to 1 lim (ln (x^{2}))

What is the derivative of x^2e^{7x} ?
The derivative of x^2e^{7x} is 2xe^{7x}+e^{7x}*7x^2
What is the first derivative of x^2e^{7x} ?
The first derivative of x^2e^{7x} is 2xe^{7x}+e^{7x}*7x^2