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

The derivative of ((3x/(x+1))^2) is (18x)/((x+1)^3)

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

The first derivative of ((3x/(x+1))^2) is (18x)/((x+1)^3)

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

\frac{18 x}{( x + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{3 x}{x + 1} \cdot \frac{3}{( x + 1 ) ^{2}} : \frac{18 x}{( x + 1 ) ^{3}}

= \frac{18 x}{( x + 1 ) ^{3}}

What is the derivative of ((3x/(x+1))^2) ?
The derivative of ((3x/(x+1))^2) is (18x)/((x+1)^3)
What is the first derivative of ((3x/(x+1))^2) ?
The first derivative of ((3x/(x+1))^2) is (18x)/((x+1)^3)