Search over 10,000 free study notes

Let u = cos xdu/dx = -sin xy = u⁴dy/du = 4u³dy/dx = dy/du * du/dx = (4u³ ) * (-sin x) = 4 cos ³ x * -sin x = -4 cos ^{3 <...}

x = -3 , x= -7

x = 1, y = 2

If the second derivative of an equation is positive (d²y /dx² > 0), we can see that this point on a curve is a minimum. This is because, where the first derivative finds the grad...

For integration by parts, the integral is uv - ∫ u' v dx. First we take u = ln x and v' = 1. While we could have u and v' be the opposite at this stage, it becomes apparent later on that we can't do this ...