How do you use the definition of a derivative to find the derivative of $f (x) = 2 x^{2} - x$ $f(x)= 2x^2-x$ ?

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How do you use the definition of a derivative to find the derivative of $f (x) = 2 x^{2} - x$ $f(x)= 2x^2-x$ ?

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Answer 1 · 2018-06-21T19:46:36

$f'(x)=4x-1$

Explanation:

$"differentiating from "color(blue)"first principles"$

$f'(x)=lim_(hto0)(f(x+h)-f(x))/h$

$color(white)(f'(x))=lim_(hto0)(2(x+h)^2-(x+h)-(2x^2-x))/h$

$color(white)(f'(x))=lim_(hto0)(2x^2+4hx+2h^2-x-h-2x^2+x)/h$

$color(white)(f'(x))=lim_(hto0)(4hx+2h^2-h)/h$

$color(white)(f'(x))=lim_(hto0)(cancel(h)(4x+2h-1))/cancel(h)$

$color(white)(xxxx)=4x-1$

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How do you use the definition of a derivative to find the derivative of $f (x) = 2 x^{2} - x$ $f(x)= 2x^2-x$ ?

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Explanation:

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How do you use the definition of a derivative to find the derivative of f(x)= 2x^2-xf(x)=2x2−xf(x)= 2x^2-x?

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How do you use the definition of a derivative to find the derivative of $f (x) = 2 x^{2} - x$ $f(x)= 2x^2-x$ ?