What is the derivative of 1/2 x^2-1/4 x+1/3 ?

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

What is the first derivative of 1/2 x^2-1/4 x+1/3 ?

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

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\frac{d}{d x} (\frac{1}{2} x^{2} - \frac{1}{4} x + \frac{1}{3})

x - \frac{1}{4}

Solution steps

\frac{d}{d x} (\frac{1}{2} x^{2} - \frac{1}{4} x + \frac{1}{3})

Simplify

\frac{1}{2} x^{2} - \frac{1}{4} x + \frac{1}{3} : \frac{x ^{2}}{2} - \frac{x}{4} + \frac{1}{3}

= \frac{d}{d x} (\frac{x ^{2}}{2} - \frac{x}{4} + \frac{1}{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{2}}{2}) - \frac{d}{d x} (\frac{x}{4}) + \frac{d}{d x} (\frac{1}{3})

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

\frac{d}{d x} (\frac{1}{3}) = 0

= x - \frac{1}{4} + 0

Simplify

= x - \frac{1}{4}

\int 4 \frac{cos ( x )}{sin ^{2} ( x )} d x

2 x^{2} - 7 x + 5

\frac{\partial}{\partial x} (C e^{2 x})

\frac{x}{x + 1}

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

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