Having trouble understanding how to solve the derivative of y=x^tanx?

[xpack]

Having trouble understanding how to solve the derivative of y=x^tanx?

Like the question says. Can someone help me please? I have an exam tomorrow and having trouble solving these.

 

[fluxions]

assuming you want dy/dx...

in general for a function like y(x) = f(x)^[g(x)], you write y(x) = exp(g(x)*ln(f(x)) then differentiate with respect to x.

 

[n!kofeyn]

Another way of viewing it is to take the natural logarithm of both sides, and then use the properties of ln to simplify things on the right hand side. Then take the derivative of both sides and solve for y'. This is the same thing that fluxions said, just a slightly different approach that I think is a little easier to work with since you don't have the exponential in the way. Just remember that (ln(y))'=y'/y.