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Math Help - Integral Differentiation

  1. #1
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    Integral Differentiation

    Can anyone please help with the following equation? (file attached).

    The 3xy2 is confusing me.

    Thanks
    Attached Thumbnails Attached Thumbnails Integral Differentiation-integral-differentiation0001.jpg  
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  2. #2
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    implicit differentiation

    Quote Originally Posted by Beginner View Post
    Can anyone please help with the following equation? (file attached).

    The 3xy^2 is confusing me.

    Thanks
    product rule. let the first function be 3x , the second y^2 ...

    3x \cdot 2y \cdot \frac{dy}{dx} + y^2 \cdot 3
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  3. #3
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    Quote Originally Posted by Beginner View Post
    Can anyone please help with the following equation? (file attached).

    The 3xy2 is confusing me.

    Thanks
    Hi! You can split 3xy^2 into 3x times y^2 and use the product rule:

     \frac{d}{dx} (3x)(y^2) = 3(y^2) + (3x) \left(2y \frac{dy}{dx} \right)
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    Quote Originally Posted by Beginner View Post
    Can anyone please help with the following equation? (file attached).

    The 3xy2 is confusing me.

    Thanks
    The equation is
    x^3 + 3xy^2 + 4y = 40
    After differentiation you get
    3x^2 + 3x(2y)(dy/dx) + 3y^2 + 4dy/dx = 0
    Now simplify to find dy/dx
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  5. #5
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    Quote Originally Posted by skeeter View Post
    product rule. let the first function be 3x , the second y^2 ...

    3x \cdot 2y \cdot \frac{dy}{dx} + y^2 \cdot 3
    Thanks for your help its much appreciated.
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  6. #6
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    Quote Originally Posted by mathemagister View Post
    Hi! You can split 3xy^2 into 3x times y^2 and use the product rule:

     \frac{d}{dx} (3x)(y^2) = 3(y^2) + (3x) \left(2y \frac{dy}{dx} \right)
    Thanks Mathemagister!
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  7. #7
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    Quote Originally Posted by sa-ri-ga-ma View Post
    The equation is
    x^3 + 3xy^2 + 4y = 40
    After differentiation you get
    3x^2 + 3x(2y)(dy/dx) + 3y^2 + 4dy/dx = 0
    Now simplify to find dy/dx
    Thanks for the help sa-ri-ga-ma
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