What is the derivative of 1/2 x+2/3 x^2 ?

The derivative of 1/2 x+2/3 x^2 is 1/2+(4x)/3

What is the first derivative of 1/2 x+2/3 x^2 ?

The first derivative of 1/2 x+2/3 x^2 is 1/2+(4x)/3

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

\frac{1}{2} + \frac{4 x}{3}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{2} + \frac{4 x}{3}

\frac{\partial}{\partial x} (x sin (y) cos (z))

y = cos (sin (x^{2}))

x \to 0 + lim (ln (x) \cdot 0)

\int \frac{x}{x - 8} d x

y^{^{''}} - 2 y^{^{'}} + 9 y = 0

What is the derivative of 1/2 x+2/3 x^2 ?
The derivative of 1/2 x+2/3 x^2 is 1/2+(4x)/3
What is the first derivative of 1/2 x+2/3 x^2 ?
The first derivative of 1/2 x+2/3 x^2 is 1/2+(4x)/3