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

The derivative of x^3+2sqrt(x)+2 is 3x^2+1/(sqrt(x))

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

The first derivative of x^3+2sqrt(x)+2 is 3x^2+1/(sqrt(x))

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

3 x^{2} + \frac{1}{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (2 x) = \frac{1}{x}

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

= 3 x^{2} + \frac{1}{x} + 0

Simplify

= 3 x^{2} + \frac{1}{x}

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