How do you find the derivative of #y = Arcsin ((3x)/4)#?
2 Answers
Explanation:
You'll need to use the chain rule. Recall that the formula for this is:
The idea is that you take the derivative of the outermost function first, and then just work your way inside.
Before we start, let's identify all our functions in this expression. We have:

#arcsin(x)# 
#(3x)/4#
Notice how we're still preserving that
And that's the end of the calculus portion to this problem! All that's left is to do some simplification to tidy up this expression, and we end up with:
If you'd like some additional help on the Chain Rule, I'd encourage you to take a look at some of my videos on the subject:
Hope that helped :)
Given:
Explanation:
Given:
Function Composition is applying one function to the results of another:
Observe that the argument of the trigonometric function
The Chain Rule is a rule for differentiating compositions of functions like the one that we have.
Chain Rule:
We are given
Let,
We will differentiate
using the common derivative result:
Using the above result we can differentiate Function.1 above as
In this step, we will differentiate the inside function
Pull the constant out
We will use the two intermediate results, Result.1 and Result.2 to proceed.
We will start with,
Substitute back
Then,
Hence, our final answer can be written as