Find the Derivative - d/dx cos(1/x)

Problem

d(cos(1/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=1/x

2. Differentiate the outer function with respect to the inner function. The derivative of cos(u) is −sin(u)

3. Differentiate the inner function. Rewrite 1/x as x(−1) and apply the Power Rule to get −1*x(−2) which is −1/(x2)

4. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

−sin(1/x)⋅(−1/(x2))

5. Simplify the expression by multiplying the negative signs and rearranging the terms.

1/(x2)*sin(1/x)

Final Answer

d(cos(1/x))/d(x)=sin(1/x)/(x2)

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