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Math Help - Differentiating a function?

  1. #1
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    Differentiating a function?

    How do I differentiate these functions? I was told I am suppose to multiply the exponent by the variable, then subtract one from the exponent, is this correct? Even if it is correct I am not sure what I am doing wrong.

    y = 3x + 2 The answer I got was 5
    y = x^2 - 2 Answer I got is 2x - 2
    y = x^3 - 2x Answer I got is 3x^2 - 2

    Can anyone give me helpful hints as to what I am doing wrong?
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  2. #2
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    Only your third answer is correct. Can you show a few more steps for the first two, so I can see exactly what isn't happening correctly?
    Last edited by mr fantastic; September 22nd 2010 at 11:50 PM.
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  3. #3
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    Quote Originally Posted by colerelm1 View Post
    How do I differentiate these functions? I was told I am suppose to multiply the exponent by the variable, then subtract one from the exponent, is this correct? Even if it is correct I am not sure what I am doing wrong.

    y = 3x + 2 The answer I got was 5
    y = x^2 - 2 Answer I got is 2x - 2
    y = x^3 - 2x Answer I got is 3x^2 - 2

    Can anyone give me helpful hints as to what I am doing wrong?
    I see what you're doing.

    you are not differentiating the constants....

    What's the derivative of a constant?
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  4. #4
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    The general rule for derivative of a power of x is
    \frac{d x^n}{dx}= n x^{n-1}

    But it is important to note that the "3" in 2x+3 can be thought of as " 3x^0 so its derivative is 3(0x^{-1})= 0. 2x= 2x^1, of course, so its derivative is 2(1x^0)= 2. The derivative of 2x+ 3 is 2(1x^0)+ 3(0x^{-1})= 2+ 0= 2.

    In my opinion, far more important than memorizing a formula like that is knowing that "the derivative is the slope of the tangent line to the graph". Since the graph of y= 2x+ 3 is a line, the derivative is just the slope, 2.

    Also important, the derivative is a "rate of change" of the function. A constant function does not change. It's derivative (rate of change) is always 0. In the first and second problems, you differentiated the constants incorrectly.
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