Question

If esin fx then dy/dx = ?​

Answer 1

Answer:

We want to find the derivative of

y=(sin(x))sin(x)

Take the logarithm on both sides

ln(y)=ln((sin(x))sin(x))

ln(y)=sin(x)⋅ln(sin(x))

Differentiate both sides using the product and chain rule

(Be aware of the implicit differentiation on the right side)

y'⋅1y=cos(x)ln(sin(x))+sin(x)cos(x)⋅1sin(x)

y'=y⋅(cos(x)ln(sin(x))+sin(x)cos(x)⋅1sin(x))

y'=y⋅(cos(x)ln(sin(x))+cos(x))

y'=y⋅cos(x)⋅(ln(sin