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

Using the product rule $\left(1 \times d 2 + 2 \times d 1\right)$, you would set 1 as ${x}^{3}$ and 2 as ${\left(2 x - 5\right)}^{4}$.
The derivative of 1 would be $3 {x}^{2}$ and the derivative of 2 is $4 {\left(2 x - 5\right)}^{3} \cdot 2$, or $8 {\left(2 x - 5\right)}^{3}$ 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).
This expanded is $112 {x}^{6} - 960 {x}^{5} + 3000 {x}^{4} - 4000 {x}^{3} + 1875 {x}^{2}$.