Derivative of Sinx with Respect to Cosx

Let u = sinx and v = cosx.

u = sinx ----> u is a function of x

v = cosx ----> 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 sinx with respect to cosx. 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 = sinx, v = cosx, ᵈᵘ⁄dₓ = cosx and ᵈⱽ⁄dₓ = -sinx.

Derivative of sinx with respect to cosx is -cotx.

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