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

The derivative of (2x^{-2}+3^{-3}) is (12x^5)/((2+3x^2)^4)

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

The first derivative of (2x^{-2}+3^{-3}) is (12x^5)/((2+3x^2)^4)

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

\frac{12 x ^{5}}{( 2 + 3 x ^{2} ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{3}{( 2 x ^{- 2} + 3 ) ^{4}} (- \frac{4}{x ^{3}}) : \frac{12 x ^{5}}{( 2 + 3 x ^{2} ) ^{4}}

= \frac{12 x ^{5}}{( 2 + 3 x ^{2} ) ^{4}}

y^{^{''}} + 9 y = cos (5 t)

y = 2 x^{2} + 3 x, (- 2, 2)

\int \frac{( sin ( 3 x ) - cos ( 2 x ) )}{4} d x

x \to - 3 lim (\frac{x ^{2} - 4}{x - 2})

x \cdot 2^{x}

What is the derivative of (2x^{-2}+3^{-3}) ?
The derivative of (2x^{-2}+3^{-3}) is (12x^5)/((2+3x^2)^4)
What is the first derivative of (2x^{-2}+3^{-3}) ?
The first derivative of (2x^{-2}+3^{-3}) is (12x^5)/((2+3x^2)^4)