[tex]\\ \sf\longmapsto \dfrac{dy}{dt}[/tex]
[tex]\\ \sf\longmapsto \dfrac{d}{dt}(3x+5)^3[/tex]
[tex]\\ \sf\longmapsto \{3(3x+5)\}^2[/tex]
[tex]\\ \sf\longmapsto (9x+15)^2[/tex]
[tex]\\ \sf\longmapsto 9x^2+2(9x)(15)+(15)^2[/tex]
[tex]\\ \sf\longmapsto 81x^2+270x+225[/tex]
Step-by-step explanation:
[tex]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[/tex]
