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Popular Calculus >

derivative of (x-y/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=2cos(2x)

d er i v a t i v e y = 2 cos (2 x)

derivative of (x+1)^{ln(x)}

d er i v a t i v e (x + 1)^{l n (x)}

integral of (x^2)/(sqrt(16-25x^2))

\int \frac{x ^{2}}{16 - 25 x ^{2}} d x

integral of ((16x))/((sqrt(x^2-9))^5)

\int \frac{( 16 x )}{( x ^{2} - 9 ) ^{5}} d x

tangent of x^2-x/5

t an g e n t x^{2} - \frac{x}{5}

Frequently Asked Questions (FAQ)

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