The discussion focuses on differentiating the function y = sin(x)^x using natural logarithms. The process involves applying the properties of logarithms and the chain rule. The key steps include rewriting the function as ln(y) = x ln(sin(x)) and then differentiating to find dy/dx, resulting in dy/dx = (sin(x))^x[ln(sin(x)) + x(cos(x)/sin(x))]. The confusion arises from understanding how the derivative of ln(sin(x)) leads to cos(x)/sin(x).
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Hello gyza502. Welcome to PF !gyza502 said:Homework Statement
Let y=sin(x)^x. Find dy/dx
My teacher said to use Natural long to solve this.
she got,
step 1:ln(y)=ln(sin(x)^x)=x ln(sin(x))
step 2:y(dy/dx)=1(ln(sin(x)+x(cos(x)/sin(x)
Final answer:dy/dx=((sin(x))^x)[ln(sin(x))+x(cos x/sin x)
I don't understand how she derived ln sin(x) to be cos(x)/sin(x)...