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Popular Calculus >

derivative of f(x)=2x^3-3x^2-72x+108

Solution

derivative of

f (x) = 2 x^{3} - 3 x^{2} - 72 x + 108

Solution

6 x^{2} - 6 x - 72

Solution steps

\frac{d}{d x} (2 x^{3} - 3 x^{2} - 72 x + 108)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (72 x) + \frac{d}{d x} (108)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (72 x) = 72

\frac{d}{d x} (108) = 0

= 6 x^{2} - 6 x - 72 + 0

Simplify

= 6 x^{2} - 6 x - 72

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=2x^3-3x^2-72x+108 ?
The derivative of f(x)=2x^3-3x^2-72x+108 is 6x^2-6x-72
What is the first derivative of f(x)=2x^3-3x^2-72x+108 ?
The first derivative of f(x)=2x^3-3x^2-72x+108 is 6x^2-6x-72