What is the derivative of-1/(y-x) ?

The derivative of-1/(y-x) is (\frac{dy)/(dx)-1}{(y-x)^2}

What is the first derivative of-1/(y-x) ?

The first derivative of-1/(y-x) is (\frac{dy)/(dx)-1}{(y-x)^2}

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Popular >

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{2}}{( x + 2 ) ^{2} ( x + 4 ) ^{2}} d x

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

\frac{d}{d x} (22 cos (x))

\frac{d}{d x} (- 2 cos (x) sin (x))

y = (2 x - 1)^{5} (1 - x^{4})^{4}

What is the derivative of-1/(y-x) ?
The derivative of-1/(y-x) is (\frac{dy)/(dx)-1}{(y-x)^2}
What is the first derivative of-1/(y-x) ?
The first derivative of-1/(y-x) is (\frac{dy)/(dx)-1}{(y-x)^2}