What is the derivative of (3x^2-6/(2x+3)) ?

The derivative of (3x^2-6/(2x+3)) is (6x^2+18x+12)/((2x+3)^2)

What is the first derivative of (3x^2-6/(2x+3)) ?

The first derivative of (3x^2-6/(2x+3)) is (6x^2+18x+12)/((2x+3)^2)

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

\frac{6 x ^{2} + 18 x + 12}{( 2 x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

6 x (2 x + 3) - 2 (3 x^{2} - 6) : 6 x^{2} + 18 x + 12

= \frac{6 x ^{2} + 18 x + 12}{( 2 x + 3 ) ^{2}}

\frac{d}{d x} (e^{x} \cdot cos (2 x))

\frac{d}{d x} (tan (x) sin (x))

4 x e^{x}

\frac{\partial}{\partial y} (4 x^{2} + y^{2} - 800)

f (x) = x^{3} - 8 x^{2}, at x = 0

What is the derivative of (3x^2-6/(2x+3)) ?
The derivative of (3x^2-6/(2x+3)) is (6x^2+18x+12)/((2x+3)^2)
What is the first derivative of (3x^2-6/(2x+3)) ?
The first derivative of (3x^2-6/(2x+3)) is (6x^2+18x+12)/((2x+3)^2)