# Using the limit definition, how do you find the derivative of #f (x) = 3x^5 + 4x #?

Apply the limit definition and use some algebra to simplify to find that

There are two equivalent definitions commonly used for the derivative of a function at a point:

and

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To find the derivative of ( f(x) = 3x^5 + 4x ) using the limit definition of a derivative, you use the formula:

[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

Substitute the function ( f(x) = 3x^5 + 4x ) into the formula and simplify the expression.

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