What is the derivative of y=(((x-2))/((x-3)))^2 ?

The derivative of y=(((x-2))/((x-3)))^2 is -(2(x-2))/((x-3)^3)

What is the first derivative of y=(((x-2))/((x-3)))^2 ?

The first derivative of y=(((x-2))/((x-3)))^2 is -(2(x-2))/((x-3)^3)

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derivative of

y = (\frac{( x - 2 )}{( x - 3 )})^{2}

- \frac{2 ( x - 2 )}{( x - 3 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{x - 2}{x - 3})^{2})

Apply the chain rule:

2 \cdot \frac{x - 2}{x - 3} \frac{d}{d x} (\frac{x - 2}{x - 3})

= 2 \cdot \frac{x - 2}{x - 3} \frac{d}{d x} (\frac{x - 2}{x - 3})

\frac{d}{d x} (\frac{x - 2}{x - 3}) = - \frac{1}{( x - 3 ) ^{2}}

= 2 \cdot \frac{x - 2}{x - 3} (- \frac{1}{( x - 3 ) ^{2}})

Simplify

2 \cdot \frac{x - 2}{x - 3} (- \frac{1}{( x - 3 ) ^{2}}) : - \frac{2 ( x - 2 )}{( x - 3 ) ^{3}}

= - \frac{2 ( x - 2 )}{( x - 3 ) ^{3}}

f (x) = 5 x + \frac{3}{x}

(4 z + e^{- z^{2}})^{5}

x \to a lim (2 x)

\int_{- \infty}^{0} x e^{2 x} d x

y^{^{''}} - y^{^{'}} - 6 y = 18 cos (3 x)

What is the derivative of y=(((x-2))/((x-3)))^2 ?
The derivative of y=(((x-2))/((x-3)))^2 is -(2(x-2))/((x-3)^3)
What is the first derivative of y=(((x-2))/((x-3)))^2 ?
The first derivative of y=(((x-2))/((x-3)))^2 is -(2(x-2))/((x-3)^3)