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Popular >

derivative of x/(4-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

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\int cos^{2} (4 x) sin (4 x) d x

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\int \frac{a}{x ^{a + 1}} d x

(\partial)/(\partial x)(x^2+y^2-2)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 2)

Frequently Asked Questions (FAQ)

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