Deriving f(x)=sec(x^2)
Mathematics

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I need help finding the derivative of f(x)=secx^2 using the double angle formula. I know that the answer is 2xsec(x^2)tan(x^2) but I don't understand how they got the answer.
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identities
Notice how a "co(something)" trig ratio is always the reciprocal of some "nonco" ratio. You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine.
sin^{2}(t) + cos^{2}(t) = 1 tan^{2}(t) + 1 = sec^{2}(t) 1 + cot^{2}(t) = csc^{2}(t)
The above, because they involve squaring and the number 1, are the "Pythagorean" identities. You can see this clearly if you consider the unit circle, where sin(t) = y, cos(t) = x, and the hypotenuse is 1.
sin(–t) = –sin(t) cos(–t) = cos(t) tan(–t) = –tan(t)
Notice in particular that sine and tangent
are odd function, while cosine is an even function
angle sum and Difference Identities
sin(α
+ β) = sin(α)cos(β) + cos(α)sin(β)
sin(α –
β) = sin(α)cos(β) – cos(α)sin(β)
cos(α +
β) = cos(α)cos(β) – sin(α)sin(β)
cos(α –
β) = cos(α)cos(β) + sin(α)sin(β)
double angle Identities
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^{2}(x) – sin^{2}(x) = 1 – 2sin^{2}(x) = 2cos^{2}(x) – 1



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