What is the derivative of sqrt((x+1/(x-5))) ?

The derivative of sqrt((x+1/(x-5))) is -3/(sqrt(x+1)(x-5)^{3/2)}

What is the first derivative of sqrt((x+1/(x-5))) ?

The first derivative of sqrt((x+1/(x-5))) is -3/(sqrt(x+1)(x-5)^{3/2)}

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\frac{d}{d x} (\frac{x + 1}{x - 5})

- \frac{3}{x + 1 ( x - 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x + 1}{x - 5})

Apply the chain rule:

\frac{1}{2 \frac{x + 1}{x - 5}} \frac{d}{d x} (\frac{x + 1}{x - 5})

= \frac{1}{2 \frac{x + 1}{x - 5}} \frac{d}{d x} (\frac{x + 1}{x - 5})

\frac{d}{d x} (\frac{x + 1}{x - 5}) = - \frac{6}{( x - 5 ) ^{2}}

= \frac{1}{2 \frac{x + 1}{x - 5}} (- \frac{6}{( x - 5 ) ^{2}})

Simplify

\frac{1}{2 \frac{x + 1}{x - 5}} (- \frac{6}{( x - 5 ) ^{2}}) : - \frac{3}{x + 1 ( x - 5 ) ^{\frac{3}{2}}}

= - \frac{3}{x + 1 ( x - 5 ) ^{\frac{3}{2}}}

3 ln (2)

x \to + 7 + lim (\frac{3}{x - 7})

y = x^{\frac{2}{3}}

\frac{d}{d x} ((x^{3} - 5 x) (x + 2))

\int \frac{x ^{\frac{1}{3}}}{x ^{\frac{4}{3}} + 4} d x

What is the derivative of sqrt((x+1/(x-5))) ?
The derivative of sqrt((x+1/(x-5))) is -3/(sqrt(x+1)(x-5)^{3/2)}
What is the first derivative of sqrt((x+1/(x-5))) ?
The first derivative of sqrt((x+1/(x-5))) is -3/(sqrt(x+1)(x-5)^{3/2)}