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Popular >

derivative of x/(sqrt(x-2))

Solution

derivative of

\frac{x}{x - 2}

Solution

\frac{x - 4}{2 ( x - 2 ) x - 2}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot x - 2 - \frac{1}{2 x - 2} x}{( x - 2 ) ^{2}} : \frac{x - 4}{2 ( x - 2 ) x - 2}

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

Popular Examples

integral from 2 to 5 of x^4ln(2x)

\int_{2}^{5} x^{4} ln (2 x) d x

integral from 0 to 18 of sqrt(t^2+2t+1)

\int_{0}^{18} t^{2} + 2 t + 1 d t

(\partial)/(\partial y)(3y-e^{sin(x)})

\frac{\partial}{\partial y} (3 y - e^{s i n (x)})

limit as x approaches 3-of (6x)/(2x-5)

x \to 3 - lim (\frac{6 x}{2 x - 5})

integral from 4 to infinity of (ln(x))/x

\int_{4}^{\infty} \frac{ln ( x )}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(x-2)) ?
The derivative of x/(sqrt(x-2)) is (x-4)/(2(x-2)sqrt(x-2))
What is the first derivative of x/(sqrt(x-2)) ?
The first derivative of x/(sqrt(x-2)) is (x-4)/(2(x-2)sqrt(x-2))