Find derivative of y=x^(tanx)

[Stuckonproblems]

This is what I have and I was wondering if you guys could check if my answer is right?

Let y = x^(tanx)
=> ln y = (tanx) ln x
=> (1/y) dy/dx = tanx d/dx (ln x) + lnx * d/dx(tanx)
=> (1/y) dy/dx = (1/x) tanx + (lnx) * sec^2 x
=> dy/dx = [x^(tanx)] * [(1/x)tanx + lnx * sec^2 x].

 

[Deleted member 4993]

This is what I have and I was wondering if you guys could check if my answer is right?

Let y = x^(tanx)
=> ln y = (tanx) ln x
=> (1/y) dy/dx = tanx d/dx (ln x) + lnx * d/dx(tanx)
=> (1/y) dy/dx = (1/x) tanx + (lnx) * sec^2 x
=> dy/dx = [x^(tanx)] * [(1/x)tanx + lnx * sec^2 x].

looks good to me......

 

[Downtrodden4]

yep

This is what I have and I was wondering if you guys could check if my answer is right?

Let y = x^(tanx)
=> ln y = (tanx) ln x
=> (1/y) dy/dx = tanx d/dx (ln x) + lnx * d/dx(tanx)
=> (1/y) dy/dx = (1/x) tanx + (lnx) * sec^2 x
=> dy/dx = [x^(tanx)] * [(1/x)tanx + lnx * sec^2 x].

Yeah, it looks perfect