Posted by **L.** on Saturday, July 5, 2008 at 10:53pm.

what is the derivative of y=4secx^2=3cotx ?

- math -
**drwls**, Sunday, July 6, 2008 at 12:25am
Is the second = supposed to be a minus? In other words, is the function

y = 4secx^2 -3cotx ?

Also, do you mean (secx)^2, or sec(x^2) ?

- math -
**L.**, Sunday, July 6, 2008 at 1:26am
Sorry about that. y=4sec(x^2)-3cotx

- math -
**drwls**, Sunday, July 6, 2008 at 7:30am
The derivative of secx is tanx*secx.

The derivative of cotx is -csc^2x

Treat sec*(x^2) as a function f of a function g(x). f(g) = sec g; g(x) = x^2

d/dx[sec(g(x))]= d/dg(secg)*dg/x

d/dx[sec(x^2)] = tanx^2)*sec(x^2)*2x

Now add them all up, and include the constant coefficients

dy/dx = 8x tan(x^2)*sec(x^2) + 3csc^2 x

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