What is the derivative of x^{-2}(5x^2-4)^3 ?

The derivative of x^{-2}(5x^2-4)^3 is -(2(5x^2-4)^3}{x^3}+\frac{30(5x^2-4)^2)/x

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

The first derivative of x^{-2}(5x^2-4)^3 is -(2(5x^2-4)^3}{x^3}+\frac{30(5x^2-4)^2)/x

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derivative of

x^{- 2} (5 x^{2} - 4)^{3}

- \frac{2 ( 5 x ^{2} - 4 ) ^{3}}{x ^{3}} + \frac{30 ( 5 x ^{2} - 4 ) ^{2}}{x}

Solution steps

\frac{d}{d x} (x^{- 2} (5 x^{2} - 4)^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = (5 x^{2} - 4)^{3}

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

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

\frac{d}{d x} ((5 x^{2} - 4)^{3}) = 30 x (5 x^{2} - 4)^{2}

= (- \frac{2}{x ^{3}}) (5 x^{2} - 4)^{3} + 30 x (5 x^{2} - 4)^{2} x^{- 2}

Simplify

(- \frac{2}{x ^{3}}) (5 x^{2} - 4)^{3} + 30 x (5 x^{2} - 4)^{2} x^{- 2} : - \frac{2 ( 5 x ^{2} - 4 ) ^{3}}{x ^{3}} + \frac{30 ( 5 x ^{2} - 4 ) ^{2}}{x}

= - \frac{2 ( 5 x ^{2} - 4 ) ^{3}}{x ^{3}} + \frac{30 ( 5 x ^{2} - 4 ) ^{2}}{x}

(2 x^{3} + x y^{2}) + (x^{2} y + 2 y^{3}) \frac{d y}{d x} = 0

\int_{0}^{t} e^{- s^{2}} d s

x \to - 5 lim (\frac{x ^{2} - 2}{5 - x})

\int \frac{x ^{3}}{3} \cdot \frac{1}{x} d x

\int \frac{- ln ( x )}{x ^{2}} d x

What is the derivative of x^{-2}(5x^2-4)^3 ?
The derivative of x^{-2}(5x^2-4)^3 is -(2(5x^2-4)^3}{x^3}+\frac{30(5x^2-4)^2)/x
What is the first derivative of x^{-2}(5x^2-4)^3 ?
The first derivative of x^{-2}(5x^2-4)^3 is -(2(5x^2-4)^3}{x^3}+\frac{30(5x^2-4)^2)/x