What is the dy/dx in terms of x and simplify the result. Need to use chain rule

Question

Use the Chain Rule to find 𝑑𝑦/𝑑𝑥 in terms of 𝑥 and simplify the result.

a. y= 1/1√1 − 𝑢² and u = cos x

b. 𝑦 = sin u and 𝑢 = √1 − 𝑥²

c. 𝑦 = 𝑒 ^−u and 𝑢 = 𝑒 ^−x

d. 𝑦 = (𝑢² + 1) ^1/2 and 𝑢 = √𝑥² − 1

Answer 1

Do you know what the chain rule is?

There appears to be a typo in part a.

I will work the 2nd one for you, then you should use it as a model to do the others.

y=sin[sqrt(1-x²)]

dy/dx=cos[sqrt(1-x²0] * 1/[2sqrt(1-x²)] * (-2x)....you simplify it.