Question

logarithmic differentiation of y=x^sinx

Answer 1

take the log of both sides first then use algebra to remove the exponents then differentiate. If you get stuck show us where.

Answer 2

\(\sf \color{}{ln(y)=ln(x^{sin(x)})}\)

Answer 3

Remember that: \(\sf \color{red}{ln(a^b)=b~ln(a)}\)

Answer 4

Which is essentially, \(product~rule\).

Answer 5

oh okay so you do use product rule between lnx and sinx

Answer 6

Yessir. Don't forget to differentiate the ln(y) also.

Answer 7

okay so i get y[(cosx)(lnx)+(sinx)(1/x)]...am i correct so far

Answer 8

Yes. And \(y\). So far so good.

Answer 9

okay so then I can't leave ln, what is my next step

Answer 10

\(\sf \color{}{y = x^{sin(x)}}\)

Answer 11

so my answer is (x^sinx)[(cosx)(lnx)+(sinx)(1/x)]?

Answer 12

Yessir.

Answer 13

cool thank you so much.