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Integrate by parts once to obtain: xe^x - e^x + c
First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our fu...
dy/dx = 2x -2 -12x^(-1/2)
We first differentiate f(x), and we get f'(x)=2x + 5. We then set this equal to 0 and then solve for x. We get that xmin= -2.5. We check whether this was indeed a minimum, by calculating the second deriva...
Figure out what skills are being tested: implicit differentiation and exponentials and logarithms.e2y = 5 - e-x2e2y(dy/dx) = e-x(dy/dx) = e-x/ 2eTCAnswered by Theodore C. • Maths tutor4145 Views
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