How do you find f'(x) using the definition of a derivative for #f(x)=3x^25x+2#?
Use algebra to simplify and evaluate the limit.
Simplify algebraically to get
That's it.
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To find ( f'(x) ) using the definition of a derivative for ( f(x)=3x^25x+2 ), follow these steps:

Start with the definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x + h)  f(x)}{h} ).

Substitute the function ( f(x) = 3x^2  5x + 2 ) into the definition.

Expand the terms ( f(x + h) ) and ( f(x) ) in the numerator.

Simplify the expression by combining like terms.

Take the limit as ( h ) approaches 0.

Evaluate the limit to find the derivative ( f'(x) ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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