How do I find the derivative of $x^{2} + 7 x - 4$ $x^2 + 7x -4$ using first principles?

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Answer 1 · 2014-10-11T01:21:52

First Principles $\to$ $->$ Difference Quotient

$f'(x)=lim_(h->0)(f(x+h)-f(x))/h$

$f(x)=x^2+7x-4$

$f(x+h)=(x+h)^2+7(x+h)-4$

$f'(x)=lim_(h->0)((x+h)^2+7(x+h)-4-(x^2+7x-4))/h$

$f'(x)=lim_(h->0)((x+h)^2+7(x+h)-4-x^2-7x+4)/h$

$f'(x)=lim_(h->0)((x+h)^2+7x+7h-4-x^2-7x+4)/h$

$f'(x)=lim_(h->0)(x^2+2xh+h^2+7x+7h-4-x^2-7x+4)/h$

$f'(x)=lim_(h->0)(2xh+h^2+7h)/h$

$f'(x)=lim_(h->0)(h(2x+h+7))/h$

$f'(x)=lim_(h->0)(2x+h+7)$

$f'(x)=2x+(0)+7$

$f'(x)=2x+7$

How do I find the derivative of x^2 + 7x -4x2+7x−4x^2 + 7x -4 using first principles?