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Setler [38]
2 years ago
15

Derivative of y=(3x+5)^3​

Mathematics
2 answers:
UkoKoshka [18]2 years ago
6 0

\\ \sf\longmapsto \dfrac{dy}{dt}

\\ \sf\longmapsto \dfrac{d}{dt}(3x+5)^3

\\ \sf\longmapsto \{3(3x+5)\}^2

\\ \sf\longmapsto (9x+15)^2

\\ \sf\longmapsto 9x^2+2(9x)(15)+(15)^2

\\ \sf\longmapsto 81x^2+270x+225

olga55 [171]2 years ago
6 0
  • \sf{81x^{2}+270x+225 }

Step-by-step explanation:

y=(3x+5)^3\\\\\dfrac{dy}{dx}=\dfrac{d}{dx}(3x+5)^3\\\\\dfrac{dy}{dx}=3(3x+5)^2×\dfrac{d}{dx}(3x+5)\\\\\dfrac{dy}{dx}=3(3x+5)^2×\dfrac{d}{dx}3x+\dfrac{d}{dx}5\\\\\dfrac{dy}{dx}=3(3x+5)^2×3+0\\\\\dfrac{dy}{dx}=9(3x+5)^2\\\\\dfrac{dy}{dx}=9(9x^2+25+30x)\\\\\dfrac{dy}{dx}=81x^2+270x+225

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