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3 years ago

Derivative of y=(3x+5)^3

Mathematics

2 answers:

UkoKoshka [18]3 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]3 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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