What is the derivative of (8sqrt(x))/x ?

The derivative of (8sqrt(x))/x is -4/(x^{3/2)}

What is the first derivative of (8sqrt(x))/x ?

The first derivative of (8sqrt(x))/x is -4/(x^{3/2)}

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derivative of

\frac{8 x}{x}

- \frac{4}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{8 x}{x})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{x}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 8 \cdot \frac{\frac{d}{d x} ( x ) x - \frac{d x}{d x} x}{x ^{2}}

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

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

= 8 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

Simplify

8 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{4}{x ^{\frac{3}{2}}}

= - \frac{4}{x ^{\frac{3}{2}}}

\int \frac{x ^{3}}{2} + \frac{1}{2 x ^{3}} d x

\int_{0}^{\frac{π}{2}} (cos (x)) d x

\int \frac{11}{12} x^{2} + \frac{1}{12} x d x

\frac{d}{d t} (sin (t))

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

What is the derivative of (8sqrt(x))/x ?
The derivative of (8sqrt(x))/x is -4/(x^{3/2)}
What is the first derivative of (8sqrt(x))/x ?
The first derivative of (8sqrt(x))/x is -4/(x^{3/2)}