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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 ...

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    ->    ...

dy/dx = (4cos(2x) + 6sin(2x) + 2)/(2+cos(2x))²

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x))^-1.  Next, find dy/dx in terms of cos(x) and sin(x). Ag...