What is the derivative of x^3+(4x^2/3-2x+5) ?

The derivative of x^3+(4x^2/3-2x+5) is 3x^2+(8x)/3-2

What is the first derivative of x^3+(4x^2/3-2x+5) ?

The first derivative of x^3+(4x^2/3-2x+5) is 3x^2+(8x)/3-2

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\frac{d}{d x} (x^{3} + \frac{4 x ^{2}}{3} - 2 x + 5)

3 x^{2} + \frac{8 x}{3} - 2

Solution steps

\frac{d}{d x} (x^{3} + \frac{4 x ^{2}}{3} - 2 x + 5)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (\frac{4 x ^{2}}{3}) - \frac{d}{d x} (2 x) + \frac{d}{d x} (5)

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

\frac{d}{d x} (\frac{4 x ^{2}}{3}) = \frac{8 x}{3}

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

\frac{d}{d x} (5) = 0

= 3 x^{2} + \frac{8 x}{3} - 2 + 0

Simplify

= 3 x^{2} + \frac{8 x}{3} - 2

What is the derivative of x^3+(4x^2/3-2x+5) ?
The derivative of x^3+(4x^2/3-2x+5) is 3x^2+(8x)/3-2
What is the first derivative of x^3+(4x^2/3-2x+5) ?
The first derivative of x^3+(4x^2/3-2x+5) is 3x^2+(8x)/3-2