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Popular >

derivative of y/(y-x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

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

Popular Examples

derivative of e^{5x+1}arccsch(sqrt(x+1))

\frac{d}{d x} (e^{5 x + 1} arccsch (x + 1))

sum from n=1 to infinity of 2/(3^{2n)}

n = 1 \sum \infty \frac{2}{3 ^{2 n}}

derivative of (11/(sqrt(x)))

\frac{d}{d x} (\frac{11}{x})

derivative of x-\sqrt[3]{x}derivative of

integral of (x^2)/(sqrt(x^2+3))

\int \frac{x ^{2}}{x ^{2} + 3} d x

Frequently Asked Questions (FAQ)

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