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Say you have two functions, A and B, and A is the gradient of B. That is to say, A is as high as B is steep (at any point). Equally, A is as high as the rate of change of B (at any point). Now let’s say w...

integral of cos²(x)*sin(x) we notice that we can use the spot the ball method here: Guessed integral: cos³(x) Differentiated Guessed Integral: -3sin(x)cos²(x), therefore o...

First, we take logs of both sides: log(5^(2x+1))=log(7) Now, using the 3rd law of logs (index rule; using the power as the coefficient), we get: (2x+1)log(5)=log(7) i.e. 2x+1 = (log(7))/(log(5)) = 1.20906...

This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first pr...

This question is an example of integrating to find the area underneath a curve between two points. We begin by intergrating the equation. Firstly, to integrate 3x² we increase the indice/power ...