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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x}{x})

Apply the Quotient Rule:

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

= 5 \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

= 5 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

Simplify

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

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

f (t) = t e^{2 t}

\int - x^{2} - 3 x d x

f (x) = 4 x^{\frac{5}{4}} + 10 x^{\frac{3}{2}} + 3 x

\int x^{5} x^{6} - 1 d x

x^{2} + 4 x + 3, y = - 1, x = 0, [- 2, 0]

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