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Friday, August 2, 2013

Derivative - Trigonometric Functions, 2

Category: Differential Calculus, Algebra, Trigonometry

"Published in Newark, California, USA"

Find the second derivative for


Solution:

Consider the given equation above


Since the denominator of the given equation contains a radical sign, then we have to rationalize the denominator in order to eliminate the radical sign as follows





But



Hence, the above equation becomes





Using the Half Angle Formula, the above equation becomes




Take the derivative on both sides of the equation with respect to x, we have





Take the derivative on both sides of the equation again with respect to x, we have







Therefore, the final answer is


Note: You must memorize or remember the trigonometric formulas and identities as much as you can so that it will be easier for you to take the derivative of trigonometric functions and equations.