Derivative of a trig function

**jmhogart** · March 24th 2009, 04:23 PM

Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.

**e^(i*pi)** · March 24th 2009, 04:26 PM

Originally Posted by jmhogart

Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.

Looks right to me

**jmhogart** · March 24th 2009, 04:31 PM

Ok thank you... now how might I go about setting the derivative equal to 0 and solving in order to find critical numbers?

**e^(i*pi)** · March 24th 2009, 04:44 PM

Originally Posted by jmhogart

Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.

Originally Posted by jmhogart

Ok thank you... now how might I go about setting the derivative equal to 0 and solving in order to find critical numbers?

f'(x)= 2cos(2x) - 2sin(x) = 0

$2cos(2x) = 2sin(x)$

We know that 2 will cancel and $cos(2x) = 1-2sin^2(x)$ . Substitute and move sin(x) back to the other side.

$1-2sin^2(x)-sin(x)=0 \rightarrow 2sin^2(x)+sin(x) - 1 = 0$

Let u = sin(x) and solve the quadratic for u then do arcsin(u).

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