Derivative of Sin Square x with Respect to Cos Square x

Let u = sin²x and v = cos²x.

u = sin²x ----> u is a function of x

v = cos²x ----> 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 cos²x. 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 = cos²x, ᵈᵘ⁄dₓ = 2 sinx cosx and ᵈⱽ⁄dₓ = - 2 sinx cosx.

Derivative of sin²x with respect to cos²x is -1.

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