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How do you find the derivative of #y=arctan(secx + tanx)#?

Answer 1

Christopher Agresta

#dy/dx=(secxtanx+sec^2x)/(1+(secx+tanx)^2)#

Rearranging:

#tany=secx+tanx#

Differentiating both sides, and recalling to use the chain rule on the left:

#sec^2y*dy/dx=secxtanx+sec^2x#

Solving for the derivative:

#dy/dx=(secxtanx+sec^2x)/sec^2y#

Using the Pythagorean identity:

#dy/dx=(secxtanx+sec^2x)/(1+tan^2y)#

Using #tany=secx+tanx#:

#dy/dx=(secxtanx+sec^2x)/(1+(secx+tanx)^2)#

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Answer 2

Emily Ammerman

To find the derivative of y=arctan(secx + tanx), apply the chain rule. The derivative is (sec^2(x) + sec(x)tan(x))/(1 + (sec(x) + tan(x))^2).

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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.