What is the derivative of (sqrt(x^5)/(x^3)) ?

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

What is the first derivative of (sqrt(x^5)/(x^3)) ?

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

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (5 x^{2} cos (x) + x)

\frac{\partial}{\partial y} (\frac{( y + x )}{( y - x )})

f (x) = x^{2} - 2

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

\int x (2 x + 7)^{8} d x

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