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

The derivative of y=3x^3+1/4 x^2 is 9x^2+x/2

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

The first derivative of y=3x^3+1/4 x^2 is 9x^2+x/2

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derivative

9 x^{2} + \frac{x}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

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

= 9 x^{2} + \frac{x}{2}

What is the derivative of y=3x^3+1/4 x^2 ?
The derivative of y=3x^3+1/4 x^2 is 9x^2+x/2
What is the first derivative of y=3x^3+1/4 x^2 ?
The first derivative of y=3x^3+1/4 x^2 is 9x^2+x/2