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

Problem

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

Solution

1. Identify the outer function as ƒ(u)=sin(u) and the inner function as u=tan(x)

2. Apply the chain rule, which states that d(ƒ(u))/d(x)=ƒ(u)^′⋅d(u)/d(x)

3. Differentiate the outer function sin(u) with respect to u to get cos(u)

4. Differentiate the inner function tan(x) with respect to x to get sec^2(x)

5. Substitute the inner function back into the derivative of the outer function and multiply the results.

Final Answer

d(sin(tan(x)))/d(x)=cos(tan(x))*sec^2(x)

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