Calculus AB : Use Derivatives of Trig Functions
Study concepts, example questions & explanations for Calculus AB
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Example Questions
Example Question #1 : Use Derivatives Of Trig Functions
Which of the following is the derivative of 
Recall that the function 
Example Question #2 : Use Derivatives Of Trig Functions
Which of the following is the derivative of 
Recall that
Example Question #3 : Use Derivatives Of Trig Functions
Which of the following is the derivative of 
Recall that
Example Question #4 : Use Derivatives Of Trig Functions
What is the derivative for 
Recall that 
Example Question #5 : Use Derivatives Of Trig Functions
True or False: We use the Chain Rule to find the derivatives of trigonometric functions.
True
False
True
This is true. The chain rule is what allows us to differentiate composite functions. Composite functions are functions that are within one another. Take 
Now for the Chain Rule we multiply the derivative of the inside function by the coefficient of the outside function while differentiating the outside function as well. 
Going back to our example of 
Example Question #6 : Use Derivatives Of Trig Functions
What is the derivative of 
We must take the derivative of both the quantity of the tangent function and tangent itself to solve for this derivative. Recall that the derivative of
Example Question #7 : Use Derivatives Of Trig Functions
What is the derivative of 
This derivative is undefined at this point
This derivative is undefined at this point
We must start this problem by finding the derivative. Recall that the derivative of the cosecant function is
Now we must find the derivative of 
And so at the point of the graph of the derivative, the function is undefined.
Example Question #1 : Use Derivatives Of Trig Functions
True or False: When the derivative of 
False
True
False
Even though we are working with trigonometric functions, the rules of derivatives remain the same. Since the graph of a derivative function is the graph of the rate of change of the original function, then when the graph of the derivative function is negative, the original function is decreasing. Even when the derivative is increasing, if it is negative the original function is still decreasing, just by less of a factor. When the derivative function is at zero, then the original function is constant. When the derivative function is positive, then the original function is increasing.
Example Question #9 : Use Derivatives Of Trig Functions
Find the derivative of 
We need to use the Chain Rule to take both the derivative of the trigonometric function and the quantity within the trig function.
Example Question #10 : Use Derivatives Of Trig Functions
What is the derivative of 
Recall that the derivative of the tangent function is 
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