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firstly, x² + 4 = 0 x² = -4 x = 2i x = -2iSecondly, x² + 8x + 25 = 0 using the quadratic formulae: x = (-b +- sqrt(b² - 4ac))/2a x = (-8+-sqrt(64-100))/2 x = -8...

To find dy/dx, the differential, of any function... you must times the coefficient of each variable of x by its power, then reduce the power by one. Using this information we can work out that 3x^4 turns ...

Firstly I would state the rule that for any composite function fg, its domain is always the domain of g. If the student would like to know why this is the case, I would simplify the expression fg(x) to f(...

We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5)
For the second part o...

Using integration by parts by letting u=x and dv/dx=e^-x. this implies that du/dx=1 and v=-e^-xThe By Parts formulae is u.v - integral(v.du/dx) = -xe^-x - in...