What is the derivative of (3x^2+1/(x+2)) ?

The derivative of (3x^2+1/(x+2)) is (3x^2+12x-1)/((x+2)^2)

What is the first derivative of (3x^2+1/(x+2)) ?

The first derivative of (3x^2+1/(x+2)) is (3x^2+12x-1)/((x+2)^2)

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

\frac{3 x ^{2} + 12 x - 1}{( x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{6 x ( x + 2 ) - 1 \cdot ( 3 x ^{2} + 1 )}{( x + 2 ) ^{2}} : \frac{3 x ^{2} + 12 x - 1}{( x + 2 ) ^{2}}

= \frac{3 x ^{2} + 12 x - 1}{( x + 2 ) ^{2}}

What is the derivative of (3x^2+1/(x+2)) ?
The derivative of (3x^2+1/(x+2)) is (3x^2+12x-1)/((x+2)^2)
What is the first derivative of (3x^2+1/(x+2)) ?
The first derivative of (3x^2+1/(x+2)) is (3x^2+12x-1)/((x+2)^2)