2 Derivative Problems?

Using the definition of the derivative find f(x)=x^2-x.

I have no problem with finding derivatives, when I dont have to use the definition. the limit being h approaching 0…

f'(x)= (f(x+h)-f(x))/h) = ([(x+h)^3-(x-h)]-(x^2-x))/h

The second one being f(x)=x^3+7x

I would like these detailed please. I have a test soon and would like to compare these examples to a few other problems I have.

Top 2 Answers

A few days ago

wayner122

Favorite Answer

I’m only going to show you the first one. Like you said you have to find the limit as h goes to 0.

numerator: (x+h)^2 -(x+h) -(x)^2 – x

= x^2 +2xh +h^2 -x -h -x^2 -x

= 2xh +h^2 -h

And you are dividing this by h, so you want the limit as h goes to 0 of (2xh +h^2 – h)/h which is the same as the limit as h goes to 0 of 2x + h -1. So the derivative is 2x -1.

4 years ago

x^2+xy+y^2 =7 Differeniate 2x + x(dy/dx) +y +2y (dy/dx) =0 (dy/dx) [ x+2y] = -(2x+y) (dy/dx) = -(2x+y) / (x+2y) At (2,a million) dy/dx= -(5)/ (4) = -5/4 Now (dy/dx) = (dy/dt) * (dt/dx) via chain policies. consequently (dt/dx) = [ (dy/dx) ] / [ (dy/dt) ] = (-5/4) / (-2) = 5/8 consequently dx/dt = a million/ (5/8) = 8/5

Is this transitive or intransitive?

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2 Derivative Problems?

2 Derivative Problems?

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