Hamilton Lyons
08/29/2023 · Junior High School
8. Use la regla de la cadena para encontrar la derivada de la función que se indica. a. Si \( y=u^{2}-2 u \) y \( u=x^{2}-x \), encuentre \( \frac{d y}{d x} \) b. Si \( y=2 u^{3}-8 u \) y \( u=x^{3}-7 x \), encuentre \( \frac{d y}{d x} \)
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Para encontrar la derivada de \( y \) con respecto a \( x \) usando la regla de la cadena, se calculan \( \frac{dy}{du} \) y \( \frac{du}{dx} \), y luego se multiplican. Para la parte a, la derivada es \( \frac{dy}{dx} = (2(x^2 - x) - 2)(2x - 1) \). Para la parte b, la derivada es \( \frac{dy}{dx} = (6(x^3 - 7x)^2 - 8)(3x^2 - 7) \).
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