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Differentiation is very helpful in the real world, in many different fields. In terms of business and economics, being able to derive maximum and minimum values of certain functions can prove extremely us...

Notice that (sin(x))'= cos(x) and (x^2)' = 2x

We use the product rule to differentiate, by noticing the expression is a product. 

so (fxgx)' = f'xgx + fx*g'x

substituting in ...

a junction between 2 neurones 

Factorise 2x²-4x-6=0

2(x²-2-3)=0   ->    2(x+1)(x-3)=0

split factors up       2=0 ,  (x+1)=0   and   (x-3)=0     

                                x+1=0  ->...

Substitute y into 4y-2=3x

4(2x-7)-2=3x   ->   8x-28-2=3x     ->      8x-3x=28+2    ->   5x=30    ->    x=30/5    ->    x=6

subsitute x into y=2x-7

y=2(6)-7    ->    ...