What is the derivative of (sqrt(x+1)-3)/(x-8) ?

The derivative of (sqrt(x+1)-3)/(x-8) is (-x+6sqrt(x+1)-10)/(2(x-8)^2sqrt(x+1))

What is the first derivative of (sqrt(x+1)-3)/(x-8) ?

The first derivative of (sqrt(x+1)-3)/(x-8) is (-x+6sqrt(x+1)-10)/(2(x-8)^2sqrt(x+1))

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derivative of

\frac{x + 1 - 3}{x - 8}

\frac{- x + 6 x + 1 - 10}{2 ( x - 8 ) ^{2} x + 1}

Solution steps

\frac{d}{d x} (\frac{x + 1 - 3}{x - 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 1 - 3 ) ( x - 8 ) - \frac{d}{d x} ( x - 8 ) ( x + 1 - 3 )}{( x - 8 ) ^{2}}

\frac{d}{d x} (x + 1 - 3) = \frac{1}{2 x + 1}

\frac{d}{d x} (x - 8) = 1

= \frac{\frac{1}{2 x + 1} ( x - 8 ) - 1 \cdot ( x + 1 - 3 )}{( x - 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x + 1} ( x - 8 ) - 1 \cdot ( x + 1 - 3 )}{( x - 8 ) ^{2}} : \frac{- x + 6 x + 1 - 10}{2 ( x - 8 ) ^{2} x + 1}

= \frac{- x + 6 x + 1 - 10}{2 ( x - 8 ) ^{2} x + 1}

\int 2 x^{\frac{1}{2}} d x

\int_{0}^{\frac{π}{2}} 2 cos^{5} (x) d x

\frac{\partial}{\partial x} (x^{a})

\frac{2 g ( x )}{1 + f ( x )}

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

What is the derivative of (sqrt(x+1)-3)/(x-8) ?
The derivative of (sqrt(x+1)-3)/(x-8) is (-x+6sqrt(x+1)-10)/(2(x-8)^2sqrt(x+1))
What is the first derivative of (sqrt(x+1)-3)/(x-8) ?
The first derivative of (sqrt(x+1)-3)/(x-8) is (-x+6sqrt(x+1)-10)/(2(x-8)^2sqrt(x+1))