Let u = sin2x and v = ecosx.
u = sin2x ----> u is a function of x
v = ecosx ----> v is a function of x
Since both u and v are the functions of x, we can find the derivatives of u and v with resepct to x.
That is, ᵈᵘ⁄dₓ and ᵈⱽ⁄dₓ.
Our aim is to find the derivative of sin2x with respect to ecosx. That is, derivative of u with respect to v.
When both u and v are the functions of x, formula to find the derivative of u with respect to v :
Substitute u = sin2x, v = ecosx, ᵈᵘ⁄dₓ = 2 sinx cosx and ᵈⱽ⁄dₓ = -sinx ecosx.
Derivative of sin2x with respect to ecosx is
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