Question

Differentiate y=sin^2 (x) + cos^2 (x)

Answer 1

So uh, any ideas? :)
Where you getting stuck?

Trig + Derivatives, does it get any more fun?
Am I right? :D

Answer 2

Yeah tons of fun...I'm not really sure where to start with the problem

Answer 3

Well we clearly will have some "chain rule" business going on.
So let's see if we can correctly identify what our "outer function" is.
The thing on the very very outside, so we can apply the steps in the correct order.

Answer 4

With trig, we put the exponent is a weird place,
so it's easy to forget that it's on the outside,\[\large\rm \sin^2x=\left(\sin x\right)^2\]So our outer function is ( )^2 something being squared.

We'll have to apply `power rule` first, ya?

Answer 5

Ok so 2(sin(x) for the first term right?

Answer 6

Good good good.
Don't forget chain rule though!

\(\large\rm \frac{d}{dx}(stuff)^2=2(stuff)\cdot\frac{d}{dx}(stuff)\)

Answer 7

\[y=\sin ^2x+\cos ^2x=1,\frac{ dy }{ dx }=0\]

Answer 8

So therefore,\[\large\rm \frac{d}{dx}(\sin x)^2=2(\sin x)\cdot(\sin x)'\]

Answer 9

Ya, applying your Pythagorean Identity makes this one a lot easier hehe :)
You can certainly do that instead if your teacher is ok with it.

Answer 10

I completely forgot about the trig identities...thank you both!

Answer 11

You want to verify the pathegorean identity by differentiating or something?

Answer 12

Tricky question, just as if they were to ask you to differentiate,

\(\color{black}{\displaystyle y=e^{2 \pi} }\)