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dy/dx = -6(0.5)x^-1.5+2
= -3x^-1.5+2
Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in ...
Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where <...
First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means: (19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction:
(19x - 2...
First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...
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