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Popular >

derivative of f(x)=(1-3x)/(6+x)

Solution

derivative of

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

Solution

- \frac{19}{( 6 + x ) ^{2}}

Solution steps

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

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

\frac{d}{d x} (6 + x) = 1

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

Simplify

\frac{( - 3 ) ( 6 + x ) - 1 \cdot ( 1 - 3 x )}{( 6 + x ) ^{2}} : - \frac{19}{( 6 + x ) ^{2}}

= - \frac{19}{( 6 + x ) ^{2}}

Popular Examples

limit as x approaches-1+of (|x+1|)/(x-1)

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(dy)/(dx)=((3y+10507))/(x-12),y(0)=47

\frac{d y}{d x} = \frac{( 3 y + 10507 )}{x - 12}, y (0) = 47

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t(dy)/(dt)+2y=t^{-3}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(1-3x)/(6+x) ?
The derivative of f(x)=(1-3x)/(6+x) is -(19)/((6+x)^2)
What is the first derivative of f(x)=(1-3x)/(6+x) ?
The first derivative of f(x)=(1-3x)/(6+x) is -(19)/((6+x)^2)