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Popular >

derivative of x/(x^4+1)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

1 \cdot (x^{4} + 1) - 4 x^{3} x = - 3 x^{4} + 1

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

Graph

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tangent of y=(x^3-16x)^{14},(4,0)tangent of

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Frequently Asked Questions (FAQ)

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