Calculus:Derivative of Trigonometric Functions

1. $f(sinx)'=cos(x)$
2. $f(cosx)'=-sin(x)$
3. $f(tanx)'=sec^{2}(x)$
4. $f(cotx)'=-csc^{2}(x)$
5. $f(cscx)'=-csc(x)cot(x)$
6. $f(secx)'=sec(x)tan(x)$

How do we get the equation

$f(sinx)'=cos(x)$ and $f(cosx)'=-sin(x)$ you only can tell by looking at the graph so we will skip it to.

So we will started with $f(tanx)'=sec^{2}(x)$

We know that $tanx={sinx \over cosx}$ If you have learn trigonometry then.

$f({sinx \over cosx})'$ by using the The Quotient Rule ${d({f \over g}) \over dx}={g{df \over dx}-f{dg \over dx} \over g^{2}}$

$f({sinx \over cosx})'={{sinx} \over {cosx}^{2}}$