Let f = cosx and g = sinx.
f = cosx ----> f is a function of x
g = sinx ----> g is a function of x
Since both f and g are the functions of x, we can find the derivatives of f and g with resepct to x.
That is, ᵈᶠ⁄dₓ and ᵈᵍ⁄dₓ.
Our aim is to find the derivative of cosx with respect to sinx. That is, derivative of f with respect to g.
When both f and g are the functions of x, formula to find the derivative of f with respect to g :
Substitute f = cosx, g = sinx, ᵈᶠ⁄dₓ = -sinx and ᵈᵍ⁄dₓ = cosx.
Derivative of cosx with respect to sinx is -tanx.
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