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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 (...

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= ...

-2/5

The best way to solve any complex problem is to start off by formulating a general overview of the problem. This is useful as it allows you to see the overall 'big' picture and allows you to really compre...

Using integration by parts, answer = 1/4x⁴lnx - 1/16x⁴ + C