How do you differentiate $g (x) = 2 {csc}^{2} x + 5 cos x$ $g(x) = 2 csc ^2x + 5 cos x$ ?

Question

2359 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-14T18:52:25

$g'(x)=-4csc^2(x)cot(x)-5sin(x)$

It helps to know some trig derivatives:

$tutorial.math.lamar.edu$

We're also going to need product rule since there's a $csc^2x$ . Rewrite $g(x)$ :

$g(x)=2csc(x)csc(x)+5cos(x)$

Now take the derivative with product rule:

$g'(x)=-2csc^2(x)cot(x)-2csc^2(x)cot(x)-5sin(x)$

Simplify:

$g'(x)=-4csc^2(x)cot(x)-5sin(x)$

How do you differentiate g(x) = 2 csc ^2x + 5 cos x g(x)=2csc2x+5cosx g(x) = 2 csc ^2x + 5 cos x ?