3.1 lists several formulas for finding derivatives that i had to memorize last year: the derivative of a constant=0, ect... These rules allow us to find short cuts when determining a function's derivative. The derivative of a^x is closely related to the original function. As values of a change, the graph of the derivative varies in its similarity to the original. When a is a certain number e, it naturally has a derivative that equals the function.
Challenges
why is f'(x) of f(x), m in the equation? I thought the derivative was the slope of the tangent, not the slope of the actual line. I do not understand logarithms in general, their relationship to derivatives,and to e.
Reflections
I memorized all these rules last year so they are familiar to me. However now that we've done some graphing first i understand why the derivative of a constant is zero. The deriv of a line is a constant, so it makes sense that if u have a constant, it would have percentage change of zero and a deriv. of zero. I was wondering if e had special implications for nature as well as logs and ln. Is it a number that is found in the ration of plants, animals, stars, ect...?
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