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Popular >

derivative of ((x^2)/(x^2+4))

Solution

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

Solution

\frac{8 x}{( x ^{2} + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x ^{2} + 4 ) - 2 x x ^{2}}{( x ^{2} + 4 ) ^{2}} : \frac{8 x}{( x ^{2} + 4 ) ^{2}}

= \frac{8 x}{( x ^{2} + 4 ) ^{2}}

Popular Examples

f(θ)=sec^2(θ)

f (θ) = sec^{2} (θ)

(\partial)/(\partial y)(4xy+4y)

\frac{\partial}{\partial y} (4 x y + 4 y)

sum from n=0 to infinity of-6(1/4)^{2n}

n = 0 \sum \infty - 6 (\frac{1}{4})^{2 n}

integral from 0 to 1 of (2x)/((x^2+3)^3)

\int_{0}^{1} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

limit as x approaches infinity of ((e^{x^4-x^2}))/2

x \to \infty lim \frac{( e ^{x^{4} - x^{2}} )}{2}

Frequently Asked Questions (FAQ)

What is the derivative of ((x^2)/(x^2+4)) ?
The derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)
What is the first derivative of ((x^2)/(x^2+4)) ?
The first derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)