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d/dx (xy) = x dy/dx + y 

d/dx (y^2) = 2y dy/dx [This is from the chain rule]

So, d/dx (2x^2 + xy + y^2 = 14) 

=> 4x + x dy/dx + y + 2y dy/dx = 0

set dy/dx = 0 as stationary ...

When dealing with complex numbers and trigonometric functions, always turn to DeMoivre's Theorem that states [cos(θ)+isin(θ)]ⁿ = [cos(nθ)+isin(nθ)]. If we set n=2, the we see a combina...

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Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2   . dx

In order to s...

To solve this question we use the product rule, where we differentiate one variable whilst keeping the other constant, and vice versa, adding the two results together to get our answer. A helpful formula ...

First we recall the general formula for the volume of revolution: V = π ∫ [f(x)]² dx Substituting our function, this gives: V = π ∫₀¹ (3^x)² x dx We could write (3^x)² as 3^(2x), or we could notice that t...