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We can differentiate the expression using the quotient rule. If f(x)=u(x)/v(x) then f'(x)=(u'(x)v(x)-u(x)v'(x))/v(x)^2. In this case u(x)=3x^2-5x so u'(x)=6x-5 and v(x)=4x^3+2x^2 so v'(x)= 12x^2+4...
Let's take for example the integral 5x2(x3-4)4dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variab...
AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2)If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + ...
Ok so for this question we'll use this example: y = (e-2x^2 + 2)1/5We start off by making the expression inside the brackets equal to u. In other words u = e-2x^2 + ...
First make a substitution so we can apply the power rule ∫xn dx = (xn+1)/(n+1) + C more simply. Can see u=x+2 means (x+2)1/2 -> u1/2 and so will help us appl...
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