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Popular >

derivative of y= 1/(x^{1/2)}

Solution

derivative of

y = \frac{1}{x ^{\frac{1}{2}}}

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

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

Popular Examples

(dy)/(dx)=(1+2y^2)/(ysin(x))

\frac{d y}{d x} = \frac{1 + 2 y ^{2}}{y sin ( x )}

integral of (3x-2)/(1-6x-9x^2)

\int \frac{3 x - 2}{1 - 6 x - 9 x ^{2}} d x

integral of (6x-5sqrt(x)+1)/(2sqrt(x))

\int \frac{6 x - 5 x + 1}{2 x} d x

derivative of (4x+5^3)

\frac{d}{d x} ((4 x + 5)^{3})

integral from 0 to 1 of ((x-sqrt(x))/3)

\int_{0}^{1} (\frac{x - x}{3}) d x

Frequently Asked Questions (FAQ)

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