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

The derivative of f(x)=(1-3x)/(1+3x) is -6/((1+3x)^2)

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

The first derivative of f(x)=(1-3x)/(1+3x) is -6/((1+3x)^2)

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derivative of

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

- \frac{6}{( 1 + 3 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 3 ) ( 1 + 3 x ) - 3 ( 1 - 3 x )}{( 1 + 3 x ) ^{2}} : - \frac{6}{( 1 + 3 x ) ^{2}}

= - \frac{6}{( 1 + 3 x ) ^{2}}

x \to \frac{3}{4} lim (\frac{4 x ^{2} - 9}{2 x - 3})

\int_{0}^{3} 3 - x d x

(4 sin (x))^{^{'}}

\int \frac{1}{49 e ^{- 9 x} + e ^{9 x}} d x

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

What is the derivative of f(x)=(1-3x)/(1+3x) ?
The derivative of f(x)=(1-3x)/(1+3x) is -6/((1+3x)^2)
What is the first derivative of f(x)=(1-3x)/(1+3x) ?
The first derivative of f(x)=(1-3x)/(1+3x) is -6/((1+3x)^2)