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Popular >

derivative of sqrt((1-x/x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 1/(x^2-2x+101)

\int \frac{1}{x ^{2} - 2 x + 101} d x

integral of sec^5(4x)

\int sec^{5} (4 x) d x

(\partial)/(\partial x)(x^{x^2+y^2})

\frac{\partial}{\partial x} (x^{x^{2} + y^{2}})

(\partial)/(\partial x)(y^6cos(4x)*4)

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

sum from n=1 to infinity of 9/(100^n)

n = 1 \sum \infty \frac{9}{10 0 ^{n}}

Frequently Asked Questions (FAQ)

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