Practice Implicit Differentiation and Derivatives of Trigonometric Inverses - The Inverse Cotangent

You know what to do.

Solution:

Step 1: Rewrite

First, remember that is the same as

Step 2: Differentiate on both sides with respect to x

Step 3: Perform chain rule on left side and use quotient rule for the cotangent

Step 4: Split fraction to get result in terms of the cotangent

Step 5: Complete the chain rule

Step 6: Substitute back in the previous equation and solve for the derivative

Step 7: We defined y = arccotan(x), substituting

Et voila.

Now that we have practiced implicit differentiation and derivatives of inverses, let's go on to
The derivative of the logarithm

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