Question

what is the differentiation of e sinx2

Answer 1

e cosx2... ...............

Answer 2

Given: esin2x.

Apply the chain rule, which states that,

dydx=dydu⋅dudx

Let u=sin2x, then we must find dudx.

Again, use the chain rule. Let z=2x,∴dzdx=2.

Then y=sinz,dydz=cosz.

Combine to get: cosz⋅2=2cosz.

Substitute back z=2x to get:

=2cos(2x)

Now, we go back to the original derivative.

From here, y=eu,∴dydu=eu, and now we can combine our results from the previous findings, where dudx=2cos2x.

∴dydx=eu⋅2cos2x

=2eucos2x

Substitute back u=sin2x to get:

=2esin2xcos2