Question

Use logarithmic differentiation to find the derivative of the function.

y=(sin(7x))^ln(x)

y'=?

Answer 1

ln(y)=In(x)[ln sin(7x)]
(1/y)dy/dx= (1/x) ln sin(7x) +[7 cos (7x)/sin(7x)].lnx
y'= y[ (1/x) ln sin (7x)+7 ln(x) .cot(7x)]
y'=[sin(7x))^ln(x) ][ (1/x) ln sin (7x)+7 ln(x) .cot(7x)]