Question

If y = ( sin x )^x , Find `dy/dx`

Answer 1

y = (sin x)^x
∴ log y = log (sin x)^x
∴ log y = x log sin x

∴ `1/y dy/dx = x  1/sin x cos x + log sin x.1`

∴ `dy/dx = y [ x cot x + log sin x ]`

∴ `dy/dx = (sin x )^x [ x cot x + log sin x ]`