derivative of ln

[proud olive]

I don't understand this problem could someone please walk my through it

[gilded idol]

You applied the product rule on 4e^(3z) which is wrong

only apply product rule on z^4 * cos(z)

[proud olive]

may i ask how come

[gilded idol]

because z^4 * cos(z) is a product and 4e^(3x) is unrelated to that product

[proud olive]

i guess i just dont know how to tell a product

[gilded idol]

if it was this case:

z^4 * [ cos(z) + 4e^(3z) ]

then you would have been right

[gilded idol]

you can do it 🙂

[proud olive]

ok

thank u

[gilded idol]

u did everything else fine 🙂

[proud olive]

wait so i just dont do anything with the 4e^3

do i just pretend it doesnt exist

[gilded idol]

you just differentiate it independently

[proud olive]

ohhhhhh

ok i think i get it

[gilded idol]

u basically got:

f(x) = ln(g(x))

=> f'(x) = g'(x)/g(x)

g(x) can be considered again a function of two parts:

Say g₁(x) = z^4 * cos(z) and g₂(x) = 4e^(3z)

g(x) = g₁(x) + g₂(x)

=> g'(x) = [g₁(x) + g₂(x)]' = g₁'(x) + g₂'(x)

[proud olive]

ok interesting

[gilded idol]

I am just trying to make it more visible if you are confused i may delete it lol

[proud olive]

yes it makes sense

thank you so much

i got it right