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#