What is the derivative of (sqrt(x+4)/(sqrt(x-1))) ?

The derivative of (sqrt(x+4)/(sqrt(x-1))) is -5/(2sqrt(x+4)(x-1)^{3/2)}

What is the first derivative of (sqrt(x+4)/(sqrt(x-1))) ?

The first derivative of (sqrt(x+4)/(sqrt(x-1))) is -5/(2sqrt(x+4)(x-1)^{3/2)}

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\frac{d}{d x} (\frac{x + 4}{x - 1})

- \frac{5}{2 x + 4 ( x - 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x + 4}{x - 1})

Simplify

\frac{x + 4}{x - 1} : \frac{x + 4}{x - 1}

= \frac{d}{d x} (\frac{x + 4}{x - 1})

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 4}{x - 1}) = - \frac{5}{( x - 1 ) ^{2}}

= \frac{1}{2 \frac{x + 4}{x - 1}} (- \frac{5}{( x - 1 ) ^{2}})

Simplify

\frac{1}{2 \frac{x + 4}{x - 1}} (- \frac{5}{( x - 1 ) ^{2}}) : - \frac{5}{2 x + 4 ( x - 1 ) ^{\frac{3}{2}}}

= - \frac{5}{2 x + 4 ( x - 1 ) ^{\frac{3}{2}}}

\frac{d}{d x} (ln (5 x + 2))

x + 12

\frac{\partial}{\partial x} (- \frac{2 y}{3 + 2 x})

\int \frac{- 28}{x ^{2} x ^{2} + 25} d x

x \to 10 lim (\frac{1}{x - 10})

What is the derivative of (sqrt(x+4)/(sqrt(x-1))) ?
The derivative of (sqrt(x+4)/(sqrt(x-1))) is -5/(2sqrt(x+4)(x-1)^{3/2)}
What is the first derivative of (sqrt(x+4)/(sqrt(x-1))) ?
The first derivative of (sqrt(x+4)/(sqrt(x-1))) is -5/(2sqrt(x+4)(x-1)^{3/2)}