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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 ...

It is used when:-Talking about something that used to happen, i.e. was ongoing for a period of time-The weather in the past-Physical description of something in the past-Talking about something that was h...

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