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Popular Calculus >

derivative of (e^x)/(x^3+1)

Solution

derivative of

\frac{e ^{x}}{x ^{3} + 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Graph

Popular Examples

integral of 1/(x(x-2)^2)

\int \frac{1}{x ( x - 2 ) ^{2}} d x

integral from 0 to infinity of 1/(x^2-1)

\int_{0}^{\infty} \frac{1}{x ^{2} - 1} d x

taylor (1+x)^{(-4)},0

t a y l or (1 + x)^{(- 4)}, 0

integral of 1/(1-x-2x^2)

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

integral from-125 to 64 of 1/(x^{1/3)}

\int_{- 125}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x)/(x^3+1) ?
The derivative of (e^x)/(x^3+1) is (e^x(x^3+1)-3x^2e^x)/((x^3+1)^2)
What is the first derivative of (e^x)/(x^3+1) ?
The first derivative of (e^x)/(x^3+1) is (e^x(x^3+1)-3x^2e^x)/((x^3+1)^2)