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The derivative of a function in a point is, by definition, the slope of the tangent line to the function in that point. In a point that is a maximum or a minimum, one can easily picture that the tangent i...

So there are many different ways of solving this equation, one being that u can find out what one of the values of x and y are and then putting the answer of the value back in the equation. The way to iso...

Answer is 2x - 4. This is found by following the standard differentiation procedure of n(ax-b)^n-1 where n was the previous power and a and b are the value inside the bracket. This means that it first goe...

Expand to get xy+3y-4x-12=x^2+y^2Rearrange to xy+3y-4x-12-x^2-y^2
Then you have to differentiate implicitly:
use product rule on xy to get:u = x v =ydu = 1 dv = dy/dx
so xy differentiates t...

1. Substitute f(x) = 53 into the equation given:f(x) = 53 = 2x² + 32).
   
   2. Rearrange to get x² on the left hand side: x² = (53-3)/2 = 253).
   
   3. Sq...