Derivative of Secx with Respect to Tanx

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.

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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