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this is implicit differentiation. We start by differentiating 3x^(2) to get 6x (lower the power by 1, multiply by the original power). For xy, we use the product rule, giving us y + (x)dy/dx (this is the ...
Imagine a function f(x)=g(x)*h(x) [that is, two functions multiplied together]
To find the derivative, f'(x)=g'(x)*h(x) + g(x)*h'(x)
For example, f(x) = (3x2)*(cos x ) ...
For this type of integral you would need to use integration by parts twice. Remember this is where the integral of u*(dv/dx)=uv-(integral with respect to x)(v*(du/dx)). For example let's say you need to i...
[Differentiate y = ln(x)] This is an example of many situations in maths where you need to solve something that is similar to what you can solve, but not in its current form. A good idea, then, i...
Let u = x^1/3
The equation can therefore be written as:
3u^2+u-2=0
This can be factorised to:
(3u-2)(u+1)+0
Therefore: u = 2/3 or u = -1 OR x^1/3 = 2/3 or x^1/3 = -1
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