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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

Popular Examples

integral of (x+5)^7

\int (x + 5)^{7} d x

limit as x approaches 0 of (sin(ax))/x

x \to 0 lim (\frac{sin ( a x )}{x})

limit as x approaches pi/2 of-cot(x)+1

x \to \frac{π}{2} lim (- cot (x) + 1)

integral of (x^2+12x+12)/(x(x+2)(x-2))

\int \frac{x ^{2} + 12 x + 12}{x ( x + 2 ) ( x - 2 )} d x

integral of 1/(3x^2)

\int \frac{1}{3 x ^{2}} d x

Frequently Asked Questions (FAQ)

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