What is the derivative of C(x)=(4x+50)/(x+2) ?

The derivative of C(x)=(4x+50)/(x+2) is -(42)/((x+2)^2)

What is the first derivative of C(x)=(4x+50)/(x+2) ?

The first derivative of C(x)=(4x+50)/(x+2) is -(42)/((x+2)^2)

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derivative of

C (x) = \frac{4 x + 50}{x + 2}

- \frac{42}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x + 50}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x + 50 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( 4 x + 50 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (4 x + 50) = 4

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

= \frac{4 ( x + 2 ) - 1 \cdot ( 4 x + 50 )}{( x + 2 ) ^{2}}

Simplify

\frac{4 ( x + 2 ) - 1 \cdot ( 4 x + 50 )}{( x + 2 ) ^{2}} : - \frac{42}{( x + 2 ) ^{2}}

= - \frac{42}{( x + 2 ) ^{2}}

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What is the derivative of C(x)=(4x+50)/(x+2) ?
The derivative of C(x)=(4x+50)/(x+2) is -(42)/((x+2)^2)
What is the first derivative of C(x)=(4x+50)/(x+2) ?
The first derivative of C(x)=(4x+50)/(x+2) is -(42)/((x+2)^2)