How do you differentiate y=x^3(2x-5)^4y=x3(2x5)4?

1 Answer
May 26, 2017

Using the product rule (1 xx d2 + 2 xx d1)(1×d2+2×d1), you would set 1 as x^3x3 and 2 as (2x-5)^4(2x5)4.

The derivative of 1 would be 3x^23x2 and the derivative of 2 is 4(2x-5)^3 *24(2x5)32, or 8(2x-5)^38(2x5)3 using the chain rule.

Now plug in the values into the product rule, so that (x^3 xx 8(2x-5)^3) + ((2x-5)^4) xx 3x^2)(x3×8(2x5)3)+((2x5)4)×3x2).

This expanded is 112 x^6 - 960 x^5 + 3000 x^4 - 4000 x^3 + 1875 x^2112x6960x5+3000x44000x3+1875x2.