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differentiate 6x^3 + 2x^2 + 1 = 18x^2 + 4x

To determine stationary point set second derivative to zero

2nd derivative =36x + 4

36x + 4 = 0 therefore x = -4/36 = -1/9

x is -ve t...

This is a question which tests your knowledge of how to use trigonometric identities as well as integration. As there is no way to immediately integrate tan^2(x) using well known trigonometric integrals a...

Differentiation is finding the slope of a graph; how steep it is at some point. In this case, we want to find out how steep the graph of x^2 is. To do this, we could look at the slope between two points o...

The area under a curve is analytically calculated using the integral of the function. The integral of the function above could be calculated using integration by parts twice, considering that 3 functions ...

Sure. If you remember how to calculate d/dx(uv) then you can understand how integration by parts works. d/dx(uv) = u(dv/dx) + v(du/dx). we can re-arrange this: u(dv/dx) = d/dx(uv) - v(du/dx). Now integrat...