      Custom Search   RADICALS To differentiate a function containing a radical, replace the radical by a fractional exponent; then find the derivative by apŁplying the appropriate theorems. EXAMPLE. Find the derivative of SOLUTION: Replace the radical by the proper fractional exŁponent, such that and by Theorem 6 EXAMPLE: Find the derivative of SOL UTION: Replace the radical by the proper fractional exŁponent, thus At this point a decision is in order. This problem may be solved by either writing and applying Theorem 6 in the denominator and then applying Theorem 5 for the quotient or writing and applying Theorem 6 for the second factor and then applying Theorem 4 for the product. The two methods of solution are completed individually as follows: Use equation (1): Find the derivative of the denominator by applying the power theorem The derivative of the numerator is Now apply Theorem 5: Multiply both numerator and denominator by and simplify: To find the same solution by a different method, use equaŁtion (2): Find the derivative of each factor: and Now apply Theorem 4: Multiply both numerator and denominator by such that, which agrees with the solution of the first method used. PRACTICE PROBLEMS: Find the derivatives of the following: ANSWERS:   Privacy Statement - Copyright Information. - Contact Us