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**delgeezee** My book says that if I learn the derivatives of sin, tangent, and secant function then I can find the rest of the trig derivatives. To do this I must replacing each function by its coresponding and put a negative on the right hand side of the new derivative equation.So I just want to make sure I have these three basic proofs down.

I can do the proofs for SinX using the f'(x) limit formula and the Addition formula for sin(a+b)...

I find the tanX by rewriting it as $\displaystyle \frac{sinX}{cosX}$ and using the quotient rule...

But when I try to find the derivative of the sec I ran into a little issue as far as factoring and rewriting

$\displaystyle \frac{d}{dx}[secX] = \frac{d}{dx}[\frac{1}{cosX}]$

Quotient rule

$\displaystyle \frac{cosX * f'(1) - (1) * f'(cosX)}{cos^2x}$

=$\displaystyle \frac{cosX * 0 - (1) * (-sinX)}{cos^2x}$

=$\displaystyle \frac{sinX}{cos^2X}$

My first instinct was to take out the sinX

$\displaystyle sinX*\frac{1}{cos^2X}$

=$\displaystyle sinXsec^2X$

But this is wrong and I am suppose to take out $\displaystyle \frac{1}{cosX}$

$\displaystyle \frac{1}{cosX}*\frac{sinX}{cosX}$

=$\displaystyle secXtanX$

This has me frustrated. Am I supposed to avoid a squared trig value unless its for the derivatives of tan and cot.