What is the derivative of x^2(2/(x^2+5/(x^3))) ?

The derivative of x^2(2/(x^2+5/(x^3))) is -5/(x^2)

What is the first derivative of x^2(2/(x^2+5/(x^3))) ?

The first derivative of x^2(2/(x^2+5/(x^3))) is -5/(x^2)

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

- \frac{5}{x ^{2}}

Solution steps

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

Simplify

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

= \frac{d}{d x} (2 + \frac{5}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2) + \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (2) = 0

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

= 0 - \frac{5}{x ^{2}}

Simplify

= - \frac{5}{x ^{2}}

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