Question

Use logarithmic differentiation to find the derivative of the function y = (cosx)^x

Answer 1

y=cos(x)^(x)

Applying log on both sides
ln(y)=xln[cos(x)]

Differentiating w.r.t x
dy/dx/y=ln[cos(x)] d/dx 1 + x d/dx 1/(cos(x)) d/dx -sin(x)
dy/dx=cos(x)^x[ln[cos(x)] -xtan(x)]