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

The derivative of f(x)=x^2(2+x^{-3}) is 4x-1/(x^2)

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

The first derivative of f(x)=x^2(2+x^{-3}) is 4x-1/(x^2)

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derivative of

f (x) = x^{2} (2 + x^{- 3})

4 x - \frac{1}{x ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 2 + x^{- 3}

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

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

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

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

Simplify

2 x (2 + x^{- 3}) + (- \frac{3}{x ^{4}}) x^{2} : 4 x - \frac{1}{x ^{2}}

= 4 x - \frac{1}{x ^{2}}

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

\int \frac{14}{x ^{2} + 1} d x

\frac{d}{d x} (e^{f (x)})

y = 10 x sin (x), (\frac{π}{2}, 5 π)

y^{^{'}} - 5 y = x

What is the derivative of f(x)=x^2(2+x^{-3}) ?
The derivative of f(x)=x^2(2+x^{-3}) is 4x-1/(x^2)
What is the first derivative of f(x)=x^2(2+x^{-3}) ?
The first derivative of f(x)=x^2(2+x^{-3}) is 4x-1/(x^2)