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Using the chain rule, we let u = sin(x) and v = x^2. Then dy/dx = udv/dx + vdu/dx. dv/dx = 2x and du/dx = cos(x). So dy/dx = sin(x)2x + x^2cos(x).

Let y = arctan(x). Then x = tan(y).

Differentiate using the chain rule and rearrange: d(x)/dx = d(tany)/dx So 1 = sec^2(y) * dy/dx dy/dx = 1/sec^2(y)

But from identity sin^2(y) + cos^2(y) = ...

[Draw Diagram] We are given the inital velocity u=11.2m/s and we know the acceleration due to gravity is 9.8m/s^2. We need to find the distance 's'. When the stone is at its highest point the velocity wil...

In this example instead of multiplying out 7 brackets it is useful to use the chain rule, which is used to differentiate the composition of more than one function. If we let what is inside the bracket equ...

In reality there's no way to know for certain and in fact some integrals can actually be proven to be impossible but they won't give you those in the exam. There's only really two main methods that you'll...