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

The derivative of f(x)=(3+x)/(1-3x) is (10)/((1-3x)^2)

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

The first derivative of f(x)=(3+x)/(1-3x) is (10)/((1-3x)^2)

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derivative of

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

\frac{10}{( 1 - 3 x ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{1 \cdot ( 1 - 3 x ) - ( - 3 ) ( 3 + x )}{( 1 - 3 x ) ^{2}} : \frac{10}{( 1 - 3 x ) ^{2}}

= \frac{10}{( 1 - 3 x ) ^{2}}

\int \frac{1}{x ^{4} - 1} d x

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

\frac{d}{d x} (x^{3} + 2 x y + y^{2} + z^{2} - 5 x - 4 z)

x \to 9 lim (\frac{81}{9 - x})

x^{2} + \frac{4}{x} - 10

What is the derivative of f(x)=(3+x)/(1-3x) ?
The derivative of f(x)=(3+x)/(1-3x) is (10)/((1-3x)^2)
What is the first derivative of f(x)=(3+x)/(1-3x) ?
The first derivative of f(x)=(3+x)/(1-3x) is (10)/((1-3x)^2)