What is the derivative of f(x)=3x^4-12x^3+9 ?

The derivative of f(x)=3x^4-12x^3+9 is 12x^3-36x^2

What is the first derivative of f(x)=3x^4-12x^3+9 ?

The first derivative of f(x)=3x^4-12x^3+9 is 12x^3-36x^2

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derivative of

f (x) = 3 x^{4} - 12 x^{3} + 9

12 x^{3} - 36 x^{2}

Solution steps

\frac{d}{d x} (3 x^{4} - 12 x^{3} + 9)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (12 x^{3}) + \frac{d}{d x} (9)

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

\frac{d}{d x} (12 x^{3}) = 36 x^{2}

\frac{d}{d x} (9) = 0

= 12 x^{3} - 36 x^{2} + 0

Simplify

= 12 x^{3} - 36 x^{2}

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What is the derivative of f(x)=3x^4-12x^3+9 ?
The derivative of f(x)=3x^4-12x^3+9 is 12x^3-36x^2
What is the first derivative of f(x)=3x^4-12x^3+9 ?
The first derivative of f(x)=3x^4-12x^3+9 is 12x^3-36x^2