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Popular >

derivative of (e^x/(x^4+1))

Solution

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 1})

Solution

\frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 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 ^{4} + 1 ) - \frac{d}{d x} ( x ^{4} + 1 ) e ^{x}}{( x ^{4} + 1 ) ^{2}}

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

\frac{d}{d x} (x^{4} + 1) = 4 x^{3}

= \frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}

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\int \frac{1}{x 4 x + 49} d x

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\int 3 sin^{4} (x co) s^{2} x d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(x^4+1)) ?
The derivative of (e^x/(x^4+1)) is (e^x(x^4+1)-4x^3e^x)/((x^4+1)^2)
What is the first derivative of (e^x/(x^4+1)) ?
The first derivative of (e^x/(x^4+1)) is (e^x(x^4+1)-4x^3e^x)/((x^4+1)^2)