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Example Questions
Example Question #11 :Derivatives Of Polar Form
Find the derivative of the following function:
The derivative of a polar function is given by
First, we must find the derivative of the function, r:
We used the following rules to find the derivative:
,
Now, plug in the derivative and the original function r into the above formula:
Example Question #12 :Derivatives Of Polar Form
Find the derivative of the following function:
The derivative (slope of the tangent line) of a polar function is given by the following formula:
So, we must simply findand plug it into the above formula:
The following rules were used to find the derivative:
,
Now, plug the given function and its derivative into the above formula to get our answer:
Example Question #31 :Parametric, Polar, And Vector Functions
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the denominator, we get:
Example Question #13 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can simplify the denominator to be
Example Question #4 :Derivatives Of Parametric, Polar, And Vector Functions
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the denominator, we get:
Example Question #14 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the numerator, we get:
Example Question #15 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Example Question #16 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the denominator, we get:
Example Question #17 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the denominator, we get:
Example Question #18 :Derivatives Of Polar Form
What is the derivative of?
In order to find the derivativeof a polar equation, we must first find the derivative ofwith respect to作为follows:
We can then swap the given values ofandinto the equation of the derivative of an expression into polar form:
Using the trigonometric identity, we can deduce that. Swapping this into the denominator, we get:
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