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Popular >

derivative of x^6e^{2x^3}

Solution

\frac{d}{d x} (x^{6} e^{2 x^{3}})

Solution

6 e^{2 x^{3}} x^{5} + 6 e^{2 x^{3}} x^{8}

Solution steps

\frac{d}{d x} (x^{6} e^{2 x^{3}})

Apply the Product Rule:

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

f = x^{6}, g = e^{2 x^{3}}

= \frac{d}{d x} (x^{6}) e^{2 x^{3}} + \frac{d}{d x} (e^{2 x^{3}}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (e^{2 x^{3}}) = e^{2 x^{3}} \cdot 6 x^{2}

= 6 x^{5} e^{2 x^{3}} + e^{2 x^{3}} \cdot 6 x^{2} x^{6}

e^{2 x^{3}} \cdot 6 x^{2} x^{6} = 6 e^{2 x^{3}} x^{8}

= 6 e^{2 x^{3}} x^{5} + 6 e^{2 x^{3}} x^{8}

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y^{^{'}} = \frac{( 3 y ^{2} + 9 )}{2 x y}

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n = 1 \sum \infty \frac{1}{2 + n}

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x \to 0 lim (\frac{1 - e ^{2 x}}{x})

integral from-infinity to 8 of re^{r/2}

\int_{- \infty}^{8} r e^{\frac{r}{2}} d r

Frequently Asked Questions (FAQ)

What is the derivative of x^6e^{2x^3} ?
The derivative of x^6e^{2x^3} is 6e^{2x^3}x^5+6e^{2x^3}x^8
What is the first derivative of x^6e^{2x^3} ?
The first derivative of x^6e^{2x^3} is 6e^{2x^3}x^5+6e^{2x^3}x^8