Question

Find an equation of the tangent line to the curve at the given point.
y = sin(sin x), (3π, 0)

Answer 1

what is y' equal to?

Answer 2

sin(sin(x))

Answer 3

y is equal to that, you have to derive both sides with respect to x to get y '

Answer 4

or dy/dx

Answer 5

use the chain rule

Answer 6

The thing is I don't understand the chain rule. I'm taking my first online class and my teacher is horrible.

Answer 7

what is the derivative of sine?

Answer 8

cosine

Answer 9

ok right
so the chain rule the derivative of the sine of something is the cosine of something, times the derivative of the something
for example,
\[\frac{d}{dx}[\sin(x^2)]=\cos(x^2)\times 2x\] and \[\frac{d}{dx}\sin(e^x)=\cos(e^x)\times e^x\]

Answer 10

in your case you have
\[\sin(\sin(x))\] so the derivative is
\[\cos(\sin(x))\times \cos(x)\]