What is the derivative of y=(x^3)/3+(x^2)/2+x/4 ?

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

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

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

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derivative of

y = \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + \frac{x}{4}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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