I have function: z=(Log[y,x])^2 where y is base of log.
I need to find differential of function z regarding the x.
My solution:
[f(g(x))]'=f'(g(x))*g'(x)
so...
[(Log[y,x])^2]'=(2*Log[y,x])*(1/(x*Ln[y]))
but math program gives me following answer:
2Ln[x]/(x*Ln[y]^2)
What is the correct answer? Is there any mistake?
Use the change of base rule to get your log into base e:
Treat as constant (because we're differentiating with respect to x)
Use the chain rule to differentiate the numerator
Since this gives the answer the book gives I don't think you have to implicitly differentiate