Finding the derivative of a function

Question

Find the derivative of the given function.

f(x)=6x³-9x+4

Answer 1

Find the derivative of f(x) = 6x³ - 9x + 4

We need three great derivative rules for this:

The Power Rule: If F(x) = xⁿ 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) = ( 6x³ - 9x + 4 )'

= (6x³)' - (9x)' + (4)' ← the derivative of a sum.

= (6∗3x²) - 9 ← the Power Rule and the derivative of a multiple

= 18x² - 9

Answer 2

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