Let f = secx and g = tanx.
f = secx ----> f is a function of x
g = tanx ----> 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.
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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 = secx, g = tanx, ᵈᶠ⁄dₓ = secxtanx and ᵈᵍ⁄dₓ = sec2x.
Derivative of secx with respect to tanx is sinx.
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