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To differentiate you must look at each term separately. So for x^2 to differentiate we bring the two down to multiply in front of the x and then take one away from the power leaving 2x. For 4x, x is to...

The chain rule works so that if you have y=f(x)g(x), where f(x) and g(x) are functions of x, dy/dx = f'(x)g(x) + f(x)g'(x)

Let A = aP + bP2 , where a and b are constants.
Sub. P = 24 , A = 36 ,
24a + 576b = 36
2a + 48b = 3 ………… (1)
Sub. P = 18 , A = 9 ,
18a + 324b = 9
2a + 36b = 1 ………… (...

First let y=ln(x).

Recall that the exponential function, e^x, is defined as the inverse of the logarithmic function, ln(x).

To make x the subject of the formula, u...

Let's start with the definition of sin(x) and cos(x). We're going to use t rather than x here to avoid confusion, but the idea is exactly the same.

Tak...