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Popular >

derivative of sqrt(e^{x^3)}

Solution

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

Solution

\frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}}}

Solution steps

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

Apply the chain rule:

\frac{1}{2 e ^{x^{3}}} \frac{d}{d x} (e^{x^{3}})

= \frac{1}{2 e ^{x^{3}}} \frac{d}{d x} (e^{x^{3}})

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

= \frac{1}{2 e ^{x^{3}}} e^{x^{3}} \cdot 3 x^{2}

Simplify

\frac{1}{2 e ^{x^{3}}} e^{x^{3}} \cdot 3 x^{2} : \frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}}}

= \frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}}}

Popular Examples

integral from-infinity to 0 of e^{7x}

\int_{- \infty}^{0} e^{7 x} d x

integral of e^x(e-1)

\int e^{x} (e - 1) d x

integral of (7x^3+8x)/(x-1)

\int \frac{7 x ^{3} + 8 x}{x - 1} d x

(ln(x+sqrt(x^2+1)))^'

(ln (x + x^{2} + 1))^{^{'}}

sum from n=0 to infinity of 7+e^{-4n}

n = 0 \sum \infty 7 + e^{- 4 n}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(e^{x^3)} ?
The derivative of sqrt(e^{x^3)} is (3e^{x^3}x^2)/(2sqrt(e^{x^3))}
What is the first derivative of sqrt(e^{x^3)} ?
The first derivative of sqrt(e^{x^3)} is (3e^{x^3}x^2)/(2sqrt(e^{x^3))}