SOLUTION: Find f’(t) for f(x) = (3x-4) (4x^3 - x^2 + 1) Find f’(t) for f(x) = x/(4x-6) Find the derivative of the function f(x) = (2x-7)/(3x-2) at x = 2. Find f’(

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find f’(t) for f(x) = (3x-4) (4x^3 - x^2 + 1) Find f’(t) for f(x) = x/(4x-6) Find the derivative of the function f(x) = (2x-7)/(3x-2) at x = 2. Find f’(      Log On


   

Question 1187926: Find f’(t) for f(x) = (3x-4) (4x^3 - x^2 + 1)

Find f’(t) for f(x) = x/(4x-6)

Find the derivative of the function f(x) = (2x-7)/(3x-2) at x = 2.

Find f’(x) for f(x) = (x^2 + 2)^3

Find dy/dx for y=ln⁡(3x^3-x^2)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


These problems are all on the same subject; but they are distinct problems and need to be submitted separately.

I will do the first....

f%28x%29+=+%283x-4%29+%284x%5E3+-+x%5E2+%2B+1%29

This function is the product of two expressions, so one method is to use the product rule:



%283x-4%29%2812x%5E2-2x%29%2B3%284x%5E3-x%5E2%2B1%29
%2836x%5E3-54x%5E2%2B8x%29%2B%2812x%5E3-3x%5E2%2B3%29
48x%5E3-57x%5E2%2B8x%2B3

Another option that in this case is easier, since it avoids use of the product rule, is to perform the indicated multiplication before taking the derivative.

f%28x%29=%283x-4%29+%284x%5E3+-+x%5E2+%2B+1%29
f%28x%29=12x%5E4-19x%5E3%2B4x%5E2%2B3x-4
df%2Fdx=48x%5E3-57x%5E2%2B8x%2B3

Post the other problems separately....