# Derivative of (sin(sin(sin(x))))

• Torshi
In summary, the derivative of d/dx (sin(sin(sin(x)))) is found by using the chain rule twice. The simplified solution is d/dx Cos(sin(sin(x)))) * Cos(sin(x)) * Cos(x). The original problem was f(x) = (sin(sin(sin(x)))), but the correct solution was ultimately obtained. Seeing a simpler example was helpful in understanding the problem.
Torshi

## Homework Statement

Derivative of d/dx (sin(sin(sin(x))))

## Homework Equations

Chain Rule twice?

## The Attempt at a Solution

d/dx Cos(sin(sin(x)))) * Cos(sin(x)) * Cos(x)

Last edited:
yes use the chain rule:

f(x)=sin(sin(x))

df/dx = cos(sin(x)) * cos(x)

jedishrfu said:
yes use the chain rule:

f(x)=sin(sin(x))

df/dx = cos(sin(x)) * cos(x)

Well the original problem was f(x) = (sin(sin(sin(x)))), but yes I believe I got it right. Thank you.

Torshi said:
Well the original problem was f(x) = (sin(sin(sin(x)))), but yes I believe I got it right. Thank you.

I know that but at first I didn't want to give you the answer outright. Later as I reread your post I saw that you had in fact the right answer. Anyway, its helpful to see a simpler example.

jedishrfu said:
I know that but at first I didn't want to give you the answer outright. Later as I reread your post I saw that you had in fact the right answer. Anyway, its helpful to see a simpler example.

Oh alrighty! Yea, when I saw the problem I was unsure at first, but then I thought I should do the chain rule. Wasn't too bad now that I think of it. Just wanted to make sure. Thanks!

## 1. What is the derivative of (sin(sin(sin(x))))?

The derivative of (sin(sin(sin(x)))) is cos(x) * cos(sin(x)) * cos(sin(sin(x))).

## 2. How do you find the derivative of (sin(sin(sin(x))))?

To find the derivative of (sin(sin(sin(x)))), you can use the chain rule and the derivative of sin(x), which is cos(x).

## 3. Is the derivative of (sin(sin(sin(x)))) the same as the derivative of sin(x)?

No, the derivative of (sin(sin(sin(x)))) is not the same as the derivative of sin(x). The derivative of sin(x) is cos(x), while the derivative of (sin(sin(sin(x)))) is cos(x) * cos(sin(x)) * cos(sin(sin(x))).

## 4. Can you simplify the derivative of (sin(sin(sin(x))))?

Yes, the derivative of (sin(sin(sin(x)))) can be simplified to cos(x) * cos(sin(x)) * cos(sin(sin(x))).

## 5. What is the significance of the derivative of (sin(sin(sin(x))))?

The derivative of (sin(sin(sin(x)))) can be used to calculate the rate of change of the function at any given point. It can also help in finding the maximum and minimum points of the function.

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