Derivative Rules

[foggy idol]

Im struggling to understand how they got this answer for this derivative

[foggy idol]

and also why is this right

i guess i dont understand derivatives of ln as a whole

[untold scroll]

just figure it our

[foggy idol]

wow you're so incredibly helpful, i shouldve thought of that sooner!

if you're not gonna provide actual help dont go in help channels

[cyan fiber]

Hi!
it's just a product rule

[2x⁵ · ln(x)]' =
= [2x⁵]' · ln(x) + [ln(x)]' · 2x⁴
= ...

The product rule says that
(fg)' = f'g + g'f

@foggy idol

Oh I didn't notice the second image
That's a chain rule
ln(x^10) = f(g(x))
f(x) = || ln(x) ||
g(x) = || x^10 ||

Chain rule:
[f(g(x))'] = f'(g(x)) · g'(x)