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Definition of derivativeUsing the definition of derivative , find the derivative of...

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Definition of derivative

Using the definition of derivative , find the derivative of f(x)=9-3x

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This problem requires the definition of derivative states that:

f'(x) = lim [f(x+h) - f(x)]/h, for h->0

We'll calculate f(x+h) = 9 - 3(x+h)

We'll remove the brackets using distributive property:

f(x+h) = 9 - 3x - 3h

We'll replace the expressions of f(x+h) and f(x) in the definition of derivative:

f'(x) = lim (9 - 3x - 3h - 9 + 3x)/h , for h->0

We'll combine and eliminate like terms:

f'(x) = lim -3h/h

We'll simplify and we'll get:

f'(x) = lim -3

f'(x) = -3

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