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The derivative of sec2x​

Sagot :

renardtnt1

Answer and Step-by-step explanation:

To find the derivative of sec(2x), we need to use the chain rule.

The chain rule is as follows:

[tex]\frac{d}{dx}[/tex][f(g(x))] = f'(g(x)) * g'(x)

What this means is that the derivative of a function with another "function" on the inside is equal to the derivative of the outside function f(x) with the inside function g(x) put back inside of f'(x), multiplied by the derivative of the inside function g(x).

Let's put this into action.

The inside function is 2x, and the outside function is sec( ).

The derivative of sec( ) is tan( )sec( ), and the derivative of 2x is 2.

[tex]\frac{d}{dx} sec(2x) = tan(2x)sec(2x) * 2[/tex]

Thus, we have our answer to be 2tan(2x)sec(2x).

I hope this helps!
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