Find the derivative of the following function showing your work and fully simplifying your answer. STEP BY STEP PLEASE!!!
f(x)=(8x-3)^5/(6x+7)^12
THANK YOU SO MUCH!!!
If we let
u = 8x-3
v = 6x+7
then we can make the expression a little easier to read during the computational steps:
f' = (5u^4*8*v^12-u^5*12v^11*6)/v^24
Now, you can cancel out v^11 top and bottom to get
f' = (40u^4*v - 72u^5)/v^13
Now factor out 4u^4 to get
f' = 4u^4(10v-18u)
= 4u^4(10(6x+7)-18(8x-3))/v^13
= 4u^4(-84x+124)/v^13
= -16u^4(21x-31)/v^13
= -16(8x-3)^4 (21x-31)/(6x+7)^13