Find the Derivative - d/dx y=tan(sin(x))

Problem

d()/d(x)*tan(sin(x))

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is tan(u) and the inner function is u=sin(x)

2. Apply the Chain Rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function. The derivative of tan(u) with respect to u is sec2(u)

4. Differentiate the inner function. The derivative of sin(x) with respect to x is cos(x)

5. Multiply the results together and substitute u=sin(x) back into the expression.

Final Answer

d(tan(sin(x)))/d(x)=sec2(sin(x))*cos(x)

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