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Let $ denote the integral symbol, as I am limited here by my keyboard.

Recall the formula for integration by parts:

$ u.(dv/dx) dx = uv - $ u(dv/dx) dx

So to find $^pi_0...

We shall differentiate each term in the equation with respect to x.

dy/dx (x²) = 2x

dy/dx (2y²) = 4y dy/dx

dy/dx (3x) = 3

So we now have the equation 2x +...

Multiply everything through by e^x   and rearrange so it equals zero
you now have e^2x -e^x-6=0
It is now similar to a quadratic equation, make the dummy substitu...

Starting from dx/dt = -axt.                                We treat dx and dt as infinitessimal factors of x and t, therefore fundemental mathematical operations still apply. Rearranging the equation to g...

The product rule is useful when you’re dealing with a function comprised of two functions multiplied together. Generally, if you have a function of the form y = f(x)g(x), then the derivative of the functi...