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Use integration by parts. Let u = x^4 and let dv/dx = -sin(x). Find du/dx = 4x^3 and fin v = cos(x). Use the equation uv - int (v du/dx) = x^4 cos(x) - 4((x^4/4)*(sin(x)) = x^4 cos(x) - x^4 sin(x) = x^4 (...

So I’ve set out a sheet with a few examples of how to do simultaneous equations. The first method shows a simple graphic representation where you can get an estimate of the solutions, but I then show how ...

Will differentiate to 3*x^(1/2)+1. As you bring down the power and mulitply it my the coefficients, and take one off of the power for terms with x. And any constant differentiates to 0.

The easiest thing to do is to look at what is in the name. For integration you have `in`, which corresponds to an `increase` in power. Whereas with differenentiation you have `d` for decrease in power. Th...

Differentiate both equations given with respect to t.
dx/dt = -2sin(t)
dy/dt = -6sin(2t)

dy/dx = (dy/dt) / (dx/dt)
Sub your values in to get

dy/dx = (3sin(2t))/sin(t)