Computing Derivatives Exercises

Answer

• Take derivatives of both sides:

Using the chain rule on the left-hand side, and the fact that the derivative of x with respect to x is 1 on the right-hand side, we find

so

Answer

• We take derivatives of both sides of the equation to find

so

Answer

• We take derivatives of both sides to find

To find the derivative of xy we need to use the product rule.

Multiply both sides by xy to remove that pesky denominator, then move all the  terms on one side and solve:

The answer

is also correct, since this is the result of multiplying our first answer by .

Answer

• Take derivatives of both sides, remembering to use the chain rule and product rule where necessary:

Now move all the  terms on one side, factor, and solve:

Answer

• This one requires the quotient rule.

Multiply both sides by x² to remove the denominator:

Then move all the terms with  to one side, factor, and solve: