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Firstly we would differentiate each equation with respect to t to find dx/dt and dy/dt- which gives us dx/dt=t and dy/dt=-4t^-2. Once you have found these you must divide dy/dt by dx/dt (or dy/dt x dt/dx)...

The question asks us to find dy/dx, in terms of x and y. Here though it is not in the form of y=f(x), but a mixed form, which we will not be able to separate out. We will have to use Implicit differentiat...

The integral of x^x can be solved by taking logarithms of the formula and getting xln(x) then using integration by parts it is given than u=ln(x) and dv=x therefore u'=1/x and v=(x^2)/2

using uv-(i...

The first step with any differentiation question is to identify which variable you are differentiating with respect to. In this case the variable is x, so we know we're looking to differentiate each term ...

This question is slightly complex and requires you to use multiple differentiation rules. Since we are differentiating a product of two functions, the first rule that we have to use is the product rule: m...