Question

Given the function: y= (3x²+2).(5x³+1)Let u- - 3x²+2 and v-5x³+11. Find du/dx (or u).(a) 6x(b)6x+2Answer [Select]2. Find dv/dx (or v)(a) 6xAnswer [Select](b)6x+23. Find dy/dx(a) 75x³+30x²+6x(d) 45x +30x²+6xAnswer [Select](c)10x(c)10x(d)15x²(d)15x²(b)75x+30x²+6x (c) 75x+30x²(e) 15x++0x²+2x(e) 10x²(e) 10x²

Answer 1

1.

`\begin{gathered} u=3x^2+2 \\ \\ (du)/(dx)=2*3x^(2-1) \\ \\ (du)/(dx)=6x \end{gathered}`Answer: a)

2.

`\begin{gathered} v=5x^3+1 \\ \\ (dv)/(dx)=3*5x^(3-1) \\ \\ (dv)/(dx)=15x^2 \end{gathered}`Answer: d)

3.

`(d)/(dx)a*b=ab^(\prime)+a^(\prime)b`
`\begin{gathered} (dy)/(dx)=(3x^2+2)(15x^2)+6x(5x^3+1) \\ \\ (dy)/(dx)=45x^4+30x^2+30x^4+6x \\ \\ (dy)/(dx)=75x^4+30x^2+6x \end{gathered}`Answer: b)