Derivative of Tanx with Respect to Secx

Let u = tanx and v = secx.

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

v = secx ----> 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 tanx with respect to secx. 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 = tanx, v = secx, ᵈᵘ⁄d = sec2x and ᵈⱽ⁄d = secxtanx.

Derivative of tanx with respect to secx is cscx.

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