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Popular >

derivative of y/(x-y)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

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

Popular Examples

tangent of f(x)= 1/(3+2x),(2, 1/7)tangent of

f (x) = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

integral of 3sin^3(x)cos^5(x)

\int 3 sin^{3} (x) cos^{5} (x) d x

derivative of (8x^2+6x+2)/(sqrt(x))derivative of

\frac{8 x ^{2} + 6 x + 2}{x}

derivative of y=(arctan(4x))^2 derivative of

y = (arctan (4 x))^{2}

integral of (x-2)/(x^2)

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

Frequently Asked Questions (FAQ)

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