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

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

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

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

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derivative of

y = \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}}}

\frac{d}{d x} (4 x^{\frac{1}{x}})

y^{^{''}} + y = 0.75 sin (t) - 0.25 sin (3 t)

\int 2 x + 4 d x

x = 2 y, x + 1 = (y - 1)^{2}

5 - x^{2}, x^{2} - 3

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