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Math Help - Derivatives question

  1. #1
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    Derivatives question

    Kindly help me with this questions.

    Obtain the derivatives for the following funtions using the delta method
    1.y=3/4
    2.y=20x^3-12x^2+4x-7/18

    Obtain the derivatives below using rules of differentiation

    1.55x^15-11e^x2+8lnx^4+8x^-15-3/4x^5/7

    2.y=(2x^3-4x^2)ln(x^4-7x^2)

    3.y=(6.8ex^3+4x^2)/(9ln(x^2-7x))

    4.y=(3e^(4x-10)4(lnx^3-2x)^7
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by aliatad View Post
    Obtain the derivatives for the following funtions using the delta method
    1.y=3/4
    2.y=20x^3-12x^2+4x-7/18
    In both cases, your expected to use the definition of the derivative : f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The first derivative should be quite easy to find and for the second one you'll need (x+h)^3=x^3+3x^2h+3xh^2+h^3 and (x+h)^2=x^2+2xh+h^2
    Obtain the derivatives below using rules of differentiation

    1.55x^15-11e^x2+8lnx^4+8x^-15-3/4x^5/7

    2.y=(2x^3-4x^2)ln(x^4-7x^2)

    3.y=(6.8ex^3+4x^2)/(9ln(x^2-7x))

    4.y=(3e^(4x-10)4(lnx^3-2x)^7
    What's the problem with these ones ?
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Hi

    In both cases, your expected to use the definition of the derivative : f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The first derivative should be quite easy to find and for the second one you'll need (x+h)^3=x^3+3x^2h+3xh^2+h^3 and (x+h)^2=x^2+2xh+h^2
    What's the problem with these ones ?
    Thanks for your help.i am so new to this kind of mathematics.with the second ones we need to use some rules which i dont know
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by aliatad View Post
    with the second ones we need to use some rules which i dont know
    Well, here are some rules that might be helpful :
    • product rule : \left(u(x)\cdot v(x)\right)'=u'(x)\cdot v(x)+v'(x)\cdot u(x)
    • quotient rule : \left(\frac{u(x)}{v(x)}\right)'=\frac{u'(x)\cdot v(x)-v'(x)\cdot u(x)}{v^2(x)}
    • chain rule : \left(u\circ v(x)\right)'=v'(x)\cdot u'\circ v(x)
    and some derivatives :
    • (x^n)'=n\cdot x^{n-1}
    • (\ln x)'=\frac{1}{x}
    • (\exp x)'=\exp x
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