4
3
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
-2
I'm not sure what you're asking. The derivative of sin(2x^2) is 4xcos(2x^x)dx.The derivative of (sin(2x^2)^2) is 8xsin(2x^2)cos(2x^2)dx.
It is -2*exp(-2x)
2x
-2
3
Well if you are talking about calculus, integration is the anti-derivative. So as my teacher explained to us, instead of going down, you will go up. For example if you have the F(x) = 2x, the F'(x) = 2. F'(x) is the derivative here, so you will do the anti of a derivative. So with the same F(x) = 2x the integral, is SF(x) = 1/3x^3. The Integral will find you the area under the curve.
d/dx sec(2x) = 2sec(2x)tan(2x)
X^n+1/n+1 X^-2/-2 0r -1/2X^-2