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Math Help - Simple Derivatives

  1. #1
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    Simple Derivatives

    Hello,

    I'm teaching myself Calculus, as I see a need for it in my future career. I started watching some basic calculus videos from MIT, but there are a few questions I would like to ask:

    I am aware of the following rule:

    \frac{dy}{dx} = nx^{n-1}

    However, I don't understand how to apply it to a function such as this:

    y = 1 - x^2

    Or this:

    y = (x^3 - 2x^2)

    I would appreciate any assistance!

    Thanks,

    Austin
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  2. #2
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    Re: Simple Derivatives

    Quote Originally Posted by ElectroNerd View Post
    Hello,

    I'm teaching myself Calculus, as I see a need for it in my future career. I started watching some basic calculus videos from MIT, but there are a few questions I would like to ask:

    I am aware of the following rule:

    \frac{dy}{dx} = nx^{n-1}

    However, I don't understand how to apply it to a function such as this:

    y = 1 - x^2

    Or this:

    y = (x^3 - 2x^2)

    I would appreciate any assistance!

    Thanks,

    Austin
    you also need to be aware that the derivative (rate of change) of a constant is 0

    y = 1 - x^2

    \frac{dy}{dx} = 0 - 2x = -2x

    for the second, just use the power rule ...

    y = x^3 - 2x^2

    \frac{dy}{dx} = 3x^2 - 4x
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  3. #3
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    Re: Simple Derivatives

    You also need to know that \frac{d(f+ g)}{dx}= \frac{df}{dx}+ \frac{dg}{dx} and \frac{d(cf)}{dx}= c \frac{df}{dx} where c is any constant.
    (You typically learn those before you learn \frac{d(x^n)}{dx}= nx^{n-1}.)

    \frac{d(1- x^2)}{dx}= \frac{d(1)}{dx}+ \frac{d(-x^2)}{dx}= \frac{(x^0)}{dx}- \frac{d(x^2)}{dx} where I have used the fact that x^0= 1 for all x except 0.

    \frac{d(x^3- 2x^2)}{dx}= \frac{d(x^3)}{dx}+ \frac{d(-2x^2)}{dx}= \frac{d(x^3)}{dx}- 2\frac{d(x^2)}{dx}
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