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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

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

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

x \to - 5 + lim (\frac{∣ x - 5 ∣}{x - 5})

\frac{d}{d x} (9 cos (x) - cos (9 x))

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

x \to 0 lim (\frac{1}{1 + x})

\frac{d}{d x} (6 x e^{- k x})

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