What is the derivative of x^2e^{6x} ?

The derivative of x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2

What is the first derivative of x^2e^{6x} ?

The first derivative of x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2

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\frac{d}{d x} (x^{2} e^{6 x})

2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{6 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{6 x}

= \frac{d}{d x} (x^{2}) e^{6 x} + \frac{d}{d x} (e^{6 x}) x^{2}

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

\int_{3}^{7} k^{2} + 2 k - 1

\frac{d}{d x} (- 5 e^{4 x})

\int cos (\frac{6}{2} t) d t

\frac{3}{s ( s ^{2} + 2 s + 5 )}

x \to 1 lim (+ (\frac{4}{2 x - 2}))

What is the derivative of x^2e^{6x} ?
The derivative of x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2
What is the first derivative of x^2e^{6x} ?
The first derivative of x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2