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Popular >

derivative of x^3+1/(x^2+3)

Solution

\frac{d}{d x} (x^{3} + \frac{1}{x ^{2}} + 3)

Solution

3 x^{2} - \frac{2}{x ^{3}}

Solution steps

\frac{d}{d x} (x^{3} + \frac{1}{x ^{2}} + 3)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (3)

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

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

\frac{d}{d x} (3) = 0

= 3 x^{2} - \frac{2}{x ^{3}} + 0

Simplify

= 3 x^{2} - \frac{2}{x ^{3}}

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Frequently Asked Questions (FAQ)

What is the derivative of x^3+1/(x^2+3) ?
The derivative of x^3+1/(x^2+3) is 3x^2-2/(x^3)
What is the first derivative of x^3+1/(x^2+3) ?
The first derivative of x^3+1/(x^2+3) is 3x^2-2/(x^3)