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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 ...

Begin by differentiating each term w.r.t x: d/dx(x^3) + d/dx(yx^2) = d/dx(y^2) + d/dx(1). the terms x^3 and 1 are simple enough to start of with: d/dx(x^3) = 3x^2 and d/dx(1) = 0. Next use the chain rule ...