What is the derivative of x^3+x^2+6/x ?

The derivative of x^3+x^2+6/x is 3x^2+2x-6/(x^2)

What is the first derivative of x^3+x^2+6/x ?

The first derivative of x^3+x^2+6/x is 3x^2+2x-6/(x^2)

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\frac{d}{d x} (x^{3} + x^{2} + \frac{6}{x})

3 x^{2} + 2 x - \frac{6}{x ^{2}}

Solution steps

\frac{d}{d x} (x^{3} + x^{2} + \frac{6}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (\frac{6}{x})

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

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

\frac{d}{d x} (\frac{6}{x}) = - \frac{6}{x ^{2}}

= 3 x^{2} + 2 x - \frac{6}{x ^{2}}

What is the derivative of x^3+x^2+6/x ?
The derivative of x^3+x^2+6/x is 3x^2+2x-6/(x^2)
What is the first derivative of x^3+x^2+6/x ?
The first derivative of x^3+x^2+6/x is 3x^2+2x-6/(x^2)