Jika y = sin ( x^3 - 3x)^3) carilah Dxy
Matematika
Aprilkupril
Pertanyaan
Jika y = sin ( x^3 - 3x)^3) carilah Dxy
1 Jawaban
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1. Jawaban nabnabs
[tex]\begin{array}{rcl}u&=&(x^3-3x)^3\\\frac{du}{dx}&=&3\times(3x^2-3)\times(x^3-3x)^2\\\frac{du}{dx}&=&(9x^2-9)(x^3-3x)^2\\\\y&=&\sin{u}\\\frac{dy}{du}&=&\cos{u}\\&=&\cos{\left(\left(x^3-3x\right)^3\right)}\\\\\frac{dy}{dx}&=&\frac{dy}{du}\times\frac{du}{dx}\\&=&\cos{\left(\left(x^3-3x\right)^3\right)}\times(9x^2-9)(x^3-3x)^2\end{array}[/tex]