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Popular >

derivative of xe^{x^5}

Solution

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

Solution

e^{x^{5}} + 5 e^{x^{5}} x^{5}

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x^{5}}

= \frac{d x}{d x} e^{x^{5}} + \frac{d}{d x} (e^{x^{5}}) x

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x^{5}} + e^{x^{5}} \cdot 5 x^{4} x

Simplify

1 \cdot e^{x^{5}} + e^{x^{5}} \cdot 5 x^{4} x : e^{x^{5}} + 5 e^{x^{5}} x^{5}

= e^{x^{5}} + 5 e^{x^{5}} x^{5}

Popular Examples

integral of cos(7x)cos(9x)

\int cos (7 x) cos (9 x) d x

limit as n approaches infinity of e^{nx}

n \to \infty lim (e^{n x})

integral of 3x^2sin(x/2)

\int 3 x^{2} sin (\frac{x}{2}) d x

integral of (sqrt(x)-e^x)

\int (x - e^{x}) d x

integral of 1/(x^2+a^2)

\int \frac{1}{x ^{2} + a ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of xe^{x^5} ?
The derivative of xe^{x^5} is e^{x^5}+5e^{x^5}x^5
What is the first derivative of xe^{x^5} ?
The first derivative of xe^{x^5} is e^{x^5}+5e^{x^5}x^5