What is the derivative of (((x+3))/(x-1))^2 ?

The derivative of (((x+3))/(x-1))^2 is -(8(x+3))/((x-1)^3)

What is the first derivative of (((x+3))/(x-1))^2 ?

The first derivative of (((x+3))/(x-1))^2 is -(8(x+3))/((x-1)^3)

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derivative of

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

- \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x + 3}{x - 1} \frac{d}{d x} (\frac{x + 3}{x - 1})

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

\frac{d}{d x} (\frac{x + 3}{x - 1}) = - \frac{4}{( x - 1 ) ^{2}}

= 2 \cdot \frac{x + 3}{x - 1} (- \frac{4}{( x - 1 ) ^{2}})

Simplify

2 \cdot \frac{x + 3}{x - 1} (- \frac{4}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

= - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

y^{^{'}} - 2 x = 4 x^{3}, y (0) = 1

7 x ln (\frac{16 x}{16 x + 1})

\frac{d y}{d x} = 2 x + 3 y

\int x \cdot e^{2 \cdot x} d x

\int \frac{1}{3 ( x + 1 )} d x

What is the derivative of (((x+3))/(x-1))^2 ?
The derivative of (((x+3))/(x-1))^2 is -(8(x+3))/((x-1)^3)
What is the first derivative of (((x+3))/(x-1))^2 ?
The first derivative of (((x+3))/(x-1))^2 is -(8(x+3))/((x-1)^3)