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Simplify the expression y = ([3]x - 2x)3 and find its derivative with respect to x.

Mathematics

ScanSolve AI Answer

Answer

-1

Step-by-step solution

2 steps
  1. Simplify the expression for yy.

    First, simplify the term inside the cube root: x−2x=−xx - 2x = -x.
    Then, substitute this back into the expression for yy:

    y=(−x3)3y = (\sqrt[3]{-x})^3

    The cube root and the cube power cancel each other out:

    y=−xy = -x
  2. Differentiate yy with respect to xx.

    We need to find dydx\frac{dy}{dx} for y=−xy = -x.
    Using the power rule for differentiation, ddx(cx)=c\frac{d}{dx}(cx) = c:

    dydx=ddx(−x)\frac{dy}{dx} = \frac{d}{dx}(-x) dydx=−1\frac{dy}{dx} = -1

    The derivative is:

    −1-1
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