If we have a function that can be expressed as a product
Rule, which is one of the fundamental ways Personally, I don't think I would normally do that last stuff, but it is good to recognize that sometimes you will do all of your calculus correctly, but the choices on multiple-choice questions might have some extra algebraic manipulation done to what you found. If you are taking AP Calculus, you will sometimes see that answer factored a little more as follows: That gets multiplied by the first factor: 18(3x-5)^5(x^2+1)^3. Now, do that same type of process for the derivative of the second multiplied by the first factor.ĭ/dx = 6(3x-5)^5(3) = 18(3x-5)^5 (Remember that Chain Rule!) That gets multiplied by the second factor: 6x(x^2+1)^2(3x-5)^6 Your two factors are (x^2 + 1 )^3 and (3x - 5 )^6 Remember your product rule: derivative of the first factor times the second, plus derivative of the second factor times the first.
