a x a x a x a x b = a4b
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(x - a) + (x - a) + (b) = 2 (x - a) + (b) = x - a + x - a + b = 2x - 2a + b
[a, b] : a ≤ x ≤ b [a, b) : a ≤ x < b (a, b] : a < x ≤ b (a, b) : a < x < b
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
x=b-a
(a x b)^b =ab x b^2 =ab^3