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Popular >

derivative of y=(sqrt(x))/x

Solution

derivative of

y = \frac{x}{x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

= \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

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

Simplify

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

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

Popular Examples

t^2y^{''}+17ty^'+64y=0

t^{2} y^{^{''}} + 17 t y^{^{'}} + 64 y = 0

limit as x approaches 0 of x(0)

x \to 0 lim (x (0))

(\partial)/(\partial y)(sin(-2x)cos(6y))

\frac{\partial}{\partial y} (sin (- 2 x) cos (6 y))

y^{''}+12y^'+36y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

derivative of tan(e^pi)

\frac{d}{d x} (tan (e^{π}))

Frequently Asked Questions (FAQ)

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