Finding the derivative is basically just finding the slope of a line tangent to a point on a curve. I think it is actually pretty easy to find the derivative of something. I think a lot of people hear the word "derivative" and talk themselves into thinking that its this really impossible math concept that they'll never understand and thats why its so hard for them to solve even simple problems. But I do think its confusing that there are so many different ways to write derivative and it can also be confusing to know which equation will work best when trying to solve a derivative problem.
Problem:
1. Find the derivative of f(x)= 3x^2 - 2x + 5
f'(x) = lim as h approaches 0 of f(x+h) - f(x)
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h
Plugging in the numbers for x and h gave me: f'(x) = lim as h approaches 0 of
3(x+h)^2 - 2(x+h) + 5 - (2x^2 + 2x + 5)
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h
Next I added like terms and did simple algebra to get: lim as h approaches 0 of 6ah + 3h^2 -2h
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h
Then I factored out h so I had: lim as h approaches 0 of
h(6a + 3h -2)
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h
The h's cancel out, because they are present in both the numerator and denominator, so I was left with the limit as h approaches 0 of (6a + 3h -2).
Then I plugged in 0 for the last remaining h, which left me with the limit as h approaches 0 = 6a-2
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