Question

Find the differential of sin²x w.r.t. e^cosx.

Answer 1

Here, suppose u = sin²x, v = e^cosx

Then, we need to differentiate u w.r. to v

i.e., `"du"/"dv" = "du"/"dx" * "dx"/"dv"`

= `("du"/"dx")/("dv"/"dx")`

= `(("d"(sin^2 x))/("dx"))/(("d"(e^(cosx)))/("dx"))`

⇒ `"du"/"dv" = (2sinx cosx)/(e^(cosx) . (-sin x))`

= `- (2 cos x)/e^(cos x)`