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P- (3,0) y=ln(x/3)     u=x/3    y=ln(u) ​​​​​​            du = 1/3  dy = 1/u = 3            dx       du dy= du x dy dx dx  du   = 1/3 x 3 = 1 gradient at normal = -1 equ...

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...