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How do you differentiate #f(x)=2secx+tanx#?

Answer 1

Ezekiel Alexander

#f'(x) =sec^2x (1 + 2sinx)#

Start by rewriting in terms of sine and cosine using the reciprocal/quotient identities.

#f(x) = 2/cosx + sinx/cosx#

#f(x) = (2 + sinx)/cosx#

We differentiate using the quotient rule.

#f'(x) = (cosx xx cosx - ( (2 + sinx)(-sinx)))/(cosx)^2#

#f'(x) = (cos^2x - (-2sinx - sin^2x))/(cosx)^2#

#f'(x) = (cos^2x + 2sinx + sin^2x)/cos^2x#

#f'(x) = (1 + 2sinx)/(cos^2x)#

#f'(x) =sec^2x (1 + 2sinx)#

Hopefully this helps!

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Answer 2

Christopher Agresta

To differentiate ( f(x) = 2\sec(x) + \tan(x) ), you can use the following steps:

Use the derivative rules:
- The derivative of ( \sec(x) ) is ( \sec(x) \tan(x) ).
- The derivative of ( \tan(x) ) is ( \sec^2(x) ).
Apply the rules to differentiate each term:
- The derivative of ( 2\sec(x) ) is ( 2\sec(x)\tan(x) ).
- The derivative of ( \tan(x) ) is ( \sec^2(x) ).
Combine the derivatives of each term to get the derivative of the function ( f(x) ):
- ( f'(x) = 2\sec(x)\tan(x) + \sec^2(x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.