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Popular >

derivative of x/(sqrt(x-9))

Solution

\frac{d}{d x} (\frac{x}{x - 9})

Solution

\frac{x - 18}{2 ( x - 9 ) x - 9}

Solution steps

\frac{d}{d x} (\frac{x}{x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x - 9 - \frac{d}{d x} ( x - 9 ) x}{( x - 9 ) ^{2}}

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

\frac{d}{d x} (x - 9) = \frac{1}{2 x - 9}

= \frac{1 \cdot x - 9 - \frac{1}{2 x - 9} x}{( x - 9 ) ^{2}}

Simplify

\frac{1 \cdot x - 9 - \frac{1}{2 x - 9} x}{( x - 9 ) ^{2}} : \frac{x - 18}{2 ( x - 9 ) x - 9}

= \frac{x - 18}{2 ( x - 9 ) x - 9}

Popular Examples

integral of ((8x-3))/(sqrt(12x-4x^2-5))

\int \frac{( 8 x - 3 )}{12 x - 4 x ^{2} - 5} d x

slope of y=-2-7x^2 slope

y = - 2 - 7 x^{2}

derivative of ((sqrt(x)-6)/(sqrt(x)+6))

\frac{d}{d x} (\frac{( x - 6 )}{x + 6})

simplify ((1+sin(t))/(1-cos(t)))^2 simplify

(\frac{1 + sin ( t )}{1 - cos ( t )})^{2}

integral from 0 to infinity of 9sin^2(x)

\int_{0}^{\infty} 9 sin^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(x-9)) ?
The derivative of x/(sqrt(x-9)) is (x-18)/(2(x-9)sqrt(x-9))
What is the first derivative of x/(sqrt(x-9)) ?
The first derivative of x/(sqrt(x-9)) is (x-18)/(2(x-9)sqrt(x-9))