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Popular Calculus >

derivative of-2/(5sqrt(x))

Solution

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

Solution

\frac{1}{5 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{1}{5 x ^{\frac{3}{2}}}

Graph

Popular Examples

derivative of (x+2/(ln(x)))

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

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

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

integral from 0 to 1 of xsqrt(1-x)

\int_{0}^{1} x 1 - x d x

solvefor x,(d^2x)/(dt^2)+x=(t^2+t)sin(t)

so l v e f or x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

slope of (-5,11),(-10,6)

s l o p e (- 5, 11), (- 10, 6)

Frequently Asked Questions (FAQ)

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