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    Hello

    How do I solve this?

    Find the derivative dy/dx of/for the following function:

    axy^b+ln(axy)=(ay+bx)^b+c, where a, b, and c are constants
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    (Original post by Lillery)
    Hello

    How do I solve this?

    Find the derivative dy/dx of/for the following function:

    axy^b+ln(axy)=(ay+bx)^b+c, where a, b, and c are constants
    if A level implicit differentiation wrt x

    if higher level move things to one side and define function φ(x,y)

    then dy/dx = - ∂φ/∂x over ∂φ/∂y
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    (Original post by Lillery)
    Hello

    How do I solve this?

    Find the derivative dy/dx of/for the following function:

    axy^b+ln(axy)=(ay+bx)^b+c, where a, b, and c are constants
    First, differentiate each term:

    axy^b differentiates to abxy^{b-1} \frac{dy}{dx} + ay^b by the product rule.

    ln(axy) differentiates to \frac{ax \frac{dy}{dx} + ay}{axy} by the chain and product rules.

    (ay+bx)^b differentiates to b(a \frac{dy}{dx} + b)(ay+bx)^{b-1} by the chain rule.

    c differentiates to 0, since it is a constant.

    This gives you the equation:
    abxy^{b-1} \frac{dy}{dx} + ay^b + \frac{ax \frac{dy}{dx} + ay}{axy} = b(a \frac{dy}{dx} + b)(ay+bx)^{b-1}

    From here, rearrange to get \frac{dy}{dx} on one side of the equation.
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    Thank you guys!
 
 
 
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Updated: October 26, 2015
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