- #1
faisal-tesla
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Homework Statement
Can someone please derive tan(2x) using the definition of the derivative?
Homework Equations
The Attempt at a Solution
I've tried to expand it but I couldn't get anywhere with it
thank you,
faisal-tesla said:yes i did, but i used the identity tan 2x = 2tanx/ (1-tan^2(x) )
after that, it got messy when i plugged in (x+h)
The definition of the derivative is the limit of the ratio of the change in the output of a function to the change in the input as the change in input approaches zero.
To derive tan(2x) using the definition of the derivative, you would use the limit definition of the derivative to find the derivative of the function. Then, you would substitute 2x for x in the derivative and simplify to get the final result.
Using the definition of the derivative allows for a rigorous and precise method of finding the derivative of a function. This is especially important for more complex functions like tan(2x), where other methods may not work.
The derivative of tan(x) is sec^2(x).
Yes, the definition of the derivative can be applied to any function, including trigonometric functions like tan(2x). This is because the definition is a general rule that can be used to find the derivative of any function.