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(1) Aim to rearrange the right hand side (rhs) to make it look like the left hand side.LHS = 2 cot (2x) + tan (x)(2) Notice that the rhs is only in terms of x, whereas the right has a function involving 2...

(1) Rearrange the equation so that the left hand side is a function of x, and the right hand side is a function of t only.dx/dt = - (5/2) x(1/x)dx = -(5/2)dt(2) Integrate both sidesln(x/A) = -(5/2)t, wher...

Logarithms allow us to calculate and manipulate indices in relation to regular numbers. The key thing to remember is that "log_xy" begs the question "wh...

y = x*ln(x)Let u = x, v = ln(x) => du/dx = 1, dv/dx = 1/x=> y = uv=> dy/dx = (du/dx)v + u(dv/dx) USING PRODUCT RULETherefore y = ln(x) + 1

We can find dz/dy using chain rule dz/dy=dz/du x du/dy (1) by defining u=3y^2+5 (since the exponent of e is a function of y we call this function u) and rewrite z=e^u. Then, we find dz/du=e^u (2) and du/d...