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By elimination:(eq1) 4x + 5y = 8(eq2) 2x + 3y = 5By eye you can see that 2x multiplied by 2 is 4x.If we multiply the whole of (eq2) by 2 we get:(eq2.1) 4x + 6y = 10(eq1) 4x + 5y = 8If we subtract the whol...

Integrate by parts once to obtain: xe^x - e^x + c

First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our fu...

The derivative of a function describes the gradient, also known as the slope. In the simplest terms, the slope defines the change in y divided by the change in x. So if there is a large increase in y for ...

dy/dx = 2x -2 -12x^(-1/2)