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Popular >

derivative of x/(sqrt(y))

Solution

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

Solution

\frac{2 y - x \frac{d y}{d x}}{2 y y}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot y - \frac{\frac{d y}{d x}}{2 y} x}{( y ) ^{2}} : \frac{2 y - x \frac{d y}{d x}}{2 y y}

= \frac{2 y - x \frac{d y}{d x}}{2 y y}

Popular Examples

integral of 4/(sqrt(x)(x+6))

\int \frac{4}{x ( x + 6 )} d x

y^'=(x^2+y^2)/(xy),y(1)=1

y^{^{'}} = \frac{x ^{2} + y ^{2}}{x y}, y (1) = 1

sum from n=1 to infinity of 8(3/4)^n

n = 1 \sum \infty 8 (\frac{3}{4})^{n}

(\partial)/(\partial x)(4x^2y^2)

\frac{\partial}{\partial x} (4 x^{2} y^{2})

slope of (-2,1),(3,-9)slope

(- 2, 1), (3, - 9)

Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(y)) ?
The derivative of x/(sqrt(y)) is (2y-x\frac{dy)/(dx)}{2ysqrt(y)}
What is the first derivative of x/(sqrt(y)) ?
The first derivative of x/(sqrt(y)) is (2y-x\frac{dy)/(dx)}{2ysqrt(y)}