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Popular >

derivative of f(x)= 1/(sqrt(x))

Solution

derivative of

f (x) = \frac{1}{x}

Solution

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

Solution steps

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

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

slope of y=-1/2 x+3 slope

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

slope of y=5x-1 slope

y = 5 x - 1

tangent of f(x)=ln(x)log_{2}(x),\at x=2 tangent of

f (x) = ln (x) lo g_{2} (x), at x = 2

tangent of f(x)= 1/(x^2)tangent of

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

derivative of f(x)=x^4 derivative of

f (x) = x^{4}

Frequently Asked Questions (FAQ)

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