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Popular >

derivative of sqrt(5/x-1)

Solution

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

Solution

- \frac{5}{2 x ^{\frac{3}{2}} - x + 5}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

tangent of f(x)=x^4-13x^2+36,\at 1 tangent of

f (x) = x^{4} - 13 x^{2} + 36, at 1

integral of (x^2-3x+2)/(x+1)

\int \frac{x ^{2} - 3 x + 2}{x + 1} d x

integral of (5y^4)/(y^5-13)

\int \frac{5 y ^{4}}{y ^{5} - 13} d y

inverse oflaplace (50s)/(s^2+25)inverse laplace

\frac{50 s}{s ^{2} + 25}

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

\frac{\partial}{\partial x} (e^{- x} y)

Frequently Asked Questions (FAQ)

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