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Popular >

derivative of f(x)= x/(x^2+11)

Solution

derivative of

f (x) = \frac{x}{x ^{2} + 11}

Solution

\frac{- x ^{2} + 11}{( x ^{2} + 11 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 11})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 11 ) - \frac{d}{d x} ( x ^{2} + 11 ) x}{( x ^{2} + 11 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 11) = 2 x

= \frac{1 \cdot ( x ^{2} + 11 ) - 2 xx}{( x ^{2} + 11 ) ^{2}}

1 \cdot (x^{2} + 11) - 2 xx = - x^{2} + 11

= \frac{- x ^{2} + 11}{( x ^{2} + 11 ) ^{2}}

Popular Examples

(\partial)/(\partial x)((x^3+2y^2)^3)

\frac{\partial}{\partial x} ((x^{3} + 2 y^{2})^{3})

limit as x approaches-infinity of 4^x+5

x \to - \infty lim (4^{x} + 5)

integral from 1 to 4 of 1/(sqrt(4x+7))

\int_{1}^{4} \frac{1}{4 x + 7} d x

derivative of ((x^2+x)(2x+1))/(4x)derivative of

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

limit as x approaches-4-of (x+2)/(x+4)

x \to - 4 - lim (\frac{x + 2}{x + 4})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x^2+11) ?
The derivative of f(x)= x/(x^2+11) is (-x^2+11)/((x^2+11)^2)
What is the first derivative of f(x)= x/(x^2+11) ?
The first derivative of f(x)= x/(x^2+11) is (-x^2+11)/((x^2+11)^2)