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We can find dy/dx by using the product rule: If y=uv then dy/dx = u (dv/dx)+ v (du/dx). In this question u= sin(6x) and v= sec(2x).So du/dx= 6cos(6x) and dv/dx=2sec(2x)tan(2x), using our rules for differe...

To differentiate xcos(2x), you first have to use the product rule, because this function is two functions (x and cos(2x) multiplied togetherNow you have x*(cos(2x))'+cos(2x)To differentiate cos(2x) you ha...

 1 + (1 + (1 + (1 + (1 + ...)^-1)^-1)^-1)^-1

This pattern goes infinitely.

The first step to this question, is to observe. Observe the patter...

First separate the variables so that the left side of the equation is an expression only in terms of y and the right side only in terms of x.exp(y)dy=sin2x dxSecondly both sides have to be integrated to o...

Using completing the square:x^2 - 6x + 11 = (x-3)^2 - (3)^2 + 11= (x - 3)^2 + 2So the turning point is (3,2). Since this curve is a positive quadratic, the turning point is a minimum the y value is 2 at i...