What is the derivative of the following function? Thank you!

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Answer 1 · 2018-06-24T13:31:51

$18x^2-9x+9=9(2x^2-x+1)$

Assuming you have: $f(x)=3x(4x^2-3x+6)1/2$ .

We first simplify the expression into:

$f(x)=1.5x(4x^2-3x+6)$

Now, we use the product rule, which states that:

$d/dx(uv)=u'v+uv'$

Let $u=1.5x,:.u'=1.5$ .

Then $v=4x^2-3x+6,v'=8x-3$ by the power rule.

Substituting back into the product rule formula, we get:

$f'(x)=1.5(4x^2-3x+6)+1.5x(8x-3)$

$=6x^2-4.5x+9+12x^2-4.5x$

$=18x^2-9x+9$