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

The derivative of (x-2^3+x) is 3x^2-12x+13

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

The first derivative of (x-2^3+x) is 3x^2-12x+13

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

3 x^{2} - 12 x + 13

Solution steps

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

Simplify

(x - 2)^{3} + x : x^{3} - 6 x^{2} + 13 x - 8

= \frac{d}{d x} (x^{3} - 6 x^{2} + 13 x - 8)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (13 x) - \frac{d}{d x} (8)

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

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (13 x) = 13

\frac{d}{d x} (8) = 0

= 3 x^{2} - 12 x + 13 - 0

Simplify

= 3 x^{2} - 12 x + 13

What is the derivative of (x-2^3+x) ?
The derivative of (x-2^3+x) is 3x^2-12x+13
What is the first derivative of (x-2^3+x) ?
The first derivative of (x-2^3+x) is 3x^2-12x+13