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We'll need to use the product rule.

Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x

Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x)

Substituting our x value gives (...

Socialists tend to support collectivism as they believe that both society and individuals benefit from a cooperative economic system. Socialists argue that humans are best able to fulfil their potential w...

First we differentiate the substitution giving, du/dx=-sinx, which is rearanged to dx=du/-sinx. we can then substitute this into the integral to get sinx e^cosx+1 du/-sinx which can be simplified to -e^co...

A) We need to find dy/dx. We know that dy/dx =(dy/dt)/(dx/dt). Differentiating each parametric equation we get: dx/dt= -2sin(2t) {using the chain rule and knowing that cos differentiates to -sin.} dy/dt= ...

The moral and psychological issues which imbue the island in “The Tempest” are exemplified by the attitudes expressed toward the island by the play’s characters. Following the storm and shipwreck of Act O...