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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 xx}{( 4 + x ^{2} ) ^{2}}

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

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

Popular Examples

limit as x approaches 0 of x^3*sin(1/x)

x \to 0 lim (x^{3} \cdot sin (\frac{1}{x}))

limit as x approaches 0 of (1-2x)^{5/x}

x \to 0 lim ((1 - 2 x)^{\frac{5}{x}})

integral of cot^2(θ)

\int cot^{2} (θ) d θ

y^{^{'}} + \frac{y}{120} = 3

integral of x^4(y-2)

\int x^{4} (y - 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)