# Finding the derivative of a function

Find the derivative of the given function.

f(x)=6x^{3}-9x+4

## 2 Answers By Expert Tutors

Dana H. answered • 01/21/20

PhD in Applied Math, teaching experience in College and High School.

Find the derivative of f(x) = 6x^{3} - 9x + 4

We need three great derivative rules for this:

The Power Rule: If F(x) = x^{n} then F'(x) = nx^{n-1}

Derivative of a multiple: If F(x) = cf(x) then F'(x) = cf'(x) c is a constant

Derivative of a sum: If F(x) = f(x) + g(x) then F'(x) = f'(x) + g'(x)

So we have

f'(x) = ( 6x^{3} - 9x + 4 )'

= (6x^{3})' - (9x)' + (4)' ← the derivative of a sum.

= (6∗3x^{2}) - 9 ← the Power Rule and the derivative of a multiple

= 18x^{2} - 9

Patrick B. answered • 01/20/20

Math and computer tutor/teacher

Indeed, 18x^2 - 9 = 9(2x^2 - 1) shall be the first derivative f'(x)

That is done by differentiating each term using the power rule as my good friend Arturo has suggested.

Happy New Year Arturo

Arturo O.

Happy New Year to you too, Patrick.01/20/20

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Arturo O.

Apply the power rule term by term.01/19/20