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

The derivative of ((3x^2-2/(2x+3))^3) is (3(3x^2-2)^2(6x^2+18x+4))/((2x+3)^4)

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

The first derivative of ((3x^2-2/(2x+3))^3) is (3(3x^2-2)^2(6x^2+18x+4))/((2x+3)^4)

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

\frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x ^{2} - 2}{2 x + 3}) = \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}}

= 3 (\frac{3 x ^{2} - 2}{2 x + 3})^{2} \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}}

Simplify

3 (\frac{3 x ^{2} - 2}{2 x + 3})^{2} \frac{6 x ^{2} + 18 x + 4}{( 2 x + 3 ) ^{2}} : \frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

= \frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

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

\int \frac{( ln ( x ^{8} ) )}{x} d x

\int sin (\frac{1}{3}) x d x

\frac{\partial}{\partial x} (9 y e^{x} - ln (z))

\frac{s + 2}{s ^{2} + 2 s + 5}

What is the derivative of ((3x^2-2/(2x+3))^3) ?
The derivative of ((3x^2-2/(2x+3))^3) is (3(3x^2-2)^2(6x^2+18x+4))/((2x+3)^4)
What is the first derivative of ((3x^2-2/(2x+3))^3) ?
The first derivative of ((3x^2-2/(2x+3))^3) is (3(3x^2-2)^2(6x^2+18x+4))/((2x+3)^4)