# 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⁄d and ᵈⱽ⁄d.

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 = cos2xᵈᵘ⁄d = 2 sinx cosx and ᵈⱽ⁄d = - 2 sinx cosx.

Derivative of sin2x with respect to cos2x is -1.

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