Find the Derivative - d/dx 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.

2. Apply the Chain Rule by differentiating the outer function cos(u) with respect to u where u=tan(x)

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

4. Differentiate the inner function u=tan(x) with respect to x which results in sec2(x)

5. Multiply the derivatives together to find the final result.

6. Substitute u=tan(x) back into the expression.

Final Answer

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

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