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Popular >

derivative of (1-e^{x^3})^5

Solution

derivative of

(1 - e^{x^{3}})^{5}

Solution

- 15 e^{x^{3}} x^{2} (1 - e^{x^{3}})^{4}

Solution steps

\frac{d}{d x} ((1 - e^{x^{3}})^{5})

Apply the chain rule:

5 (1 - e^{x^{3}})^{4} \frac{d}{d x} (1 - e^{x^{3}})

= 5 (1 - e^{x^{3}})^{4} \frac{d}{d x} (1 - e^{x^{3}})

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

= 5 (1 - e^{x^{3}})^{4} (- 3 e^{x^{3}} x^{2})

Simplify

= - 15 e^{x^{3}} x^{2} (1 - e^{x^{3}})^{4}

Popular Examples

limit as x approaches 1-of x^2-2

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

tangent of y=(x^2-1)/(x^2+x+1),(1,0)tangent of

y = \frac{x ^{2} - 1}{x ^{2} + x + 1}, (1, 0)

y^{''}+4y^'+5y=cos(2x)

y^{^{''}} + 4 y^{^{'}} + 5 y = cos (2 x)

inverse oflaplace 1/((x^2+1)*x)inverse laplace

\frac{1}{( x ^{2} + 1 ) \cdot x}

integral of xsin(1/4 x)

\int x sin (\frac{1}{4} x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (1-e^{x^3})^5 ?
The derivative of (1-e^{x^3})^5 is -15e^{x^3}x^2(1-e^{x^3})^4
What is the first derivative of (1-e^{x^3})^5 ?
The first derivative of (1-e^{x^3})^5 is -15e^{x^3}x^2(1-e^{x^3})^4