What is the derivative of f(x)=(1-4x)/(3+x) ?

The derivative of f(x)=(1-4x)/(3+x) is -(13)/((3+x)^2)

What is the first derivative of f(x)=(1-4x)/(3+x) ?

The first derivative of f(x)=(1-4x)/(3+x) is -(13)/((3+x)^2)

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derivative of

f (x) = \frac{1 - 4 x}{3 + x}

- \frac{13}{( 3 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 4 x}{3 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 4 x ) ( 3 + x ) - \frac{d}{d x} ( 3 + x ) ( 1 - 4 x )}{( 3 + x ) ^{2}}

\frac{d}{d x} (1 - 4 x) = - 4

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

= \frac{( - 4 ) ( 3 + x ) - 1 \cdot ( 1 - 4 x )}{( 3 + x ) ^{2}}

Simplify

\frac{( - 4 ) ( 3 + x ) - 1 \cdot ( 1 - 4 x )}{( 3 + x ) ^{2}} : - \frac{13}{( 3 + x ) ^{2}}

= - \frac{13}{( 3 + x ) ^{2}}

x \to 5 lim (ln (x - 4) + \frac{1}{2})

\int n o n e d x

\int \frac{e ^{\frac{1}{x ^{3}}}}{x ^{4}} d x

\frac{\partial}{\partial x} (8 x^{2} cos (5) x^{3})

\frac{d}{d x} (\frac{ln ( x )}{e ^{x}})

What is the derivative of f(x)=(1-4x)/(3+x) ?
The derivative of f(x)=(1-4x)/(3+x) is -(13)/((3+x)^2)
What is the first derivative of f(x)=(1-4x)/(3+x) ?
The first derivative of f(x)=(1-4x)/(3+x) is -(13)/((3+x)^2)