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Popular >

derivative of (x^2/(x-11))

Solution

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

Solution

\frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 11) = 1

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

Simplify

\frac{2 x ( x - 11 ) - 1 \cdot x ^{2}}{( x - 11 ) ^{2}} : \frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

= \frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

Graph

Popular Examples

normal of y= 2/(4x),(4,4)normal of

y = \frac{2}{4 x}, (4, 4)

limit as x approaches infinity of 2/x+4x

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

limit as y approaches infinity of 1/y

y \to \infty lim (\frac{1}{y})

derivative of 3x+4/x derivative of

3 x + \frac{4}{x}

(dy)/(dx)=((x^2+y^2))/(x^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(x-11)) ?
The derivative of (x^2/(x-11)) is (x^2-22x)/((x-11)^2)
What is the first derivative of (x^2/(x-11)) ?
The first derivative of (x^2/(x-11)) is (x^2-22x)/((x-11)^2)