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

Problem

d(cos(tan(x)))/d(x)

Solution

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

2. Apply the Chain Rule by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

3. Differentiate the outer function cos(u) which results in −sin(u)

4. Differentiate the inner function tan(x) which results in sec2(x)

5. Substitute the inner function back into the expression and combine the results.

Final Answer

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

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