Question

can someone explain the difference between du/dv and dv/dx so I can understand the chain rule better??

Answer 1

ok.... if you have


y = (2x + 5)^5

the way to approch it is to do some substitution

let u = 2x + 5

so you are looking at

y = u^5

find the derivative of y with respect to u dy/du

dy/du = 5u^4

but you also need to deal with the 2x + 5 since it is equal to u

so you need to differentiate u with respect to x du/dx

du/dx = 2

so to find dy/dx

you need to use the chain rule

dy/dx = dy/du * du/dx

= 5(u)^4 * 2

make the substitution for u

dy/dx = 10(2x + 5)^4

hope this helps

Answer 2

Thank you so much!