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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int - 3 tan (\frac{x}{3}) d x

\int_{3}^{7} (x - 6) x - 3 d x

\int_{1}^{e} 1

\int \frac{x ^{3}}{1 + x ^{2}} d x

x^{- \frac{1}{4}} + x^{\frac{1}{4}}

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