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Tag: quotient rule

calculus

Calculus: why the derivative of tanx is (secx)^2

Jack May 6, 2024 Tagged with derivative, quotient rule, trig derivatives, verifying differentiation formula

Tutoring calculus, everyday formulas students count on can often be verified. The tutor mentions the derivative of tanx. It’s true that (tanx)’ = (secx)^2. But why? Realizing tanx = sinx/cosx, then using the the quotient rule (u/v)’ = (vu’ – …

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calculus

Calculus: proving derivative of tan: quotient rule

Jack Nov 14, 2016 Tagged with differentiate tanx, quotient rule

The tutor shows how to remind yourself that the derivative of tanx is sec2x. Let’s imagine you don’t recall that (tanx)’=sec2x. Here’s how to reconstruct it: Recall that tanx=sinx/cosx Take the derivative of sinx/cosx using the quotient rule:(u/v)’ = (vu’-uv’)/v2 …

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