What is the derivative of (sqrt(x)/(x-10)) ?

The derivative of (sqrt(x)/(x-10)) is (-x-10)/(2sqrt(x)(x-10)^2)

What is the first derivative of (sqrt(x)/(x-10)) ?

The first derivative of (sqrt(x)/(x-10)) is (-x-10)/(2sqrt(x)(x-10)^2)

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\frac{d}{d x} (\frac{x}{x - 10})

\frac{- x - 10}{2 x ( x - 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 10})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( x - 10 ) - \frac{d}{d x} ( x - 10 ) x}{( x - 10 ) ^{2}}

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

\frac{d}{d x} (x - 10) = 1

= \frac{\frac{1}{2 x} ( x - 10 ) - 1 \cdot x}{( x - 10 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x - 10 ) - 1 \cdot x}{( x - 10 ) ^{2}} : \frac{- x - 10}{2 x ( x - 10 ) ^{2}}

= \frac{- x - 10}{2 x ( x - 10 ) ^{2}}

ln (1 - z)

\int 3 x^{2} - 24 x + 48 d x

\int \frac{x ^{2} - 7 x - 12}{x ( x ^{2} + 3 x + 3 )} d x

\frac{d}{d x} (3 x^{4} - 8 x^{3} + 2)

f (x) = - 5 x^{2} - 6 x + 200

What is the derivative of (sqrt(x)/(x-10)) ?
The derivative of (sqrt(x)/(x-10)) is (-x-10)/(2sqrt(x)(x-10)^2)
What is the first derivative of (sqrt(x)/(x-10)) ?
The first derivative of (sqrt(x)/(x-10)) is (-x-10)/(2sqrt(x)(x-10)^2)