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Find dy/dx of the function 10x^2+4y^2=sqrt(7).

Is the answer 20x+8y=0

  • Calculus -

    No; that is not the right answer.

    Differentiate both sides of the equation with respect to x. Because y is a function of x, this is called "implicit differentiation". You get
    20 x + 8 y dy/dx = 0

    Solve that for dy/dx

    dy/dx = -20x/8y = -(5/2)(y/x)

    Note that you did not have to solve for y(x) first to obtain this result for dy/dx. That is why implicit differentiation is so convenient.

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