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Differentiating is a process which you can apply to a function which lets you find the gradient (or slope) the function.

The first part of the question is actually a "show that" the equation in the question can be rearranged to the form 10 cot^(x) + 11 cot(x) - 6 = 0. To do this add 11 cot (x) and subtract 16 to/f...

(x^x)(ln(x)+1)

u² = 2 + xx = u² - 2dx/du = 2u
ʃ x(2 + x))^1/2 dx= ʃ xu dx= ʃ u(u² - 2) dx= ʃ 2u² (u² - 2) du= ʃ 2u⁴ - 4u² du= [...

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x...