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

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

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

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

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derivative of

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

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

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

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

Simplify

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

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

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