If y = t² and t = x + 3 then (dy)/(dx) is equal to:

If $y = t^2$ and $t = x + 3$ then $\frac{dy}{dx}$ is equal to:

(a)$(x + 3)^2$
(b)$2(x + 3)$
(c)$2t$
(d)$2(x + 3)^2$

Answer

Correct option: (b)

Answer: (b) $2(x + 3)$ $y=t^2$ gives $\frac{dy}{dt}=2t$ and $t=x+3$ gives $\frac{dt}{dx}=1$. Hence $\frac{dy}{dx}=2t=2(x+3)$, which is option (b) (option (c) $2t$ is the same value written in $t$). The question is in terms of $x$, so (b) is chosen.