Find the Derivative - d/dx sin(sin(sin(x)))

Problem

d(sin(sin(sin(x))))/d(x)

Solution

1. Identify the structure of the function as a composition of three functions, which requires the repeated application of the chain rule.

2. Apply the chain rule to the outermost sine function, where the derivative of sin(u) is cos(u)

d(sin(sin(sin(x))))/d(x)=cos(sin(sin(x)))⋅d(sin(sin(x)))/d(x)

3. Apply the chain rule again to the inner composition sin(sin(x))

d(sin(sin(x)))/d(x)=cos(sin(x))⋅d(sin(x))/d(x)

4. Differentiate the innermost function sin(x) which results in cos(x)

d(sin(x))/d(x)=cos(x)

5. Combine all the factors obtained from the chain rule steps to find the final derivative.

cos(sin(sin(x)))⋅cos(sin(x))⋅cos(x)

Final Answer

d(sin(sin(sin(x))))/d(x)=cos(sin(sin(x)))*cos(sin(x))*cos(x)

Want more problems? Check here!