If y = u + 1 - $81 / 3$ and u = $\frac { t } { 6 }$ + 1, find $\frac { d y } { d t }$ .
A) $\frac { 1 } { 6 }$
B) - $\frac { 1 } { 6 t ^ { 2 } }$ ∙ $8 - 2 / 3$
C) - $\frac { t ^ { 2 } } { 6 }$
D) -2 ∙ $8 - 2 / 3$

Question

Quizplus · Accepted Answer

To find $\frac { d y } { d t }$, we first substitute $u = \frac { t } { 6 } + 1$ into $y = u + 1 - 81 / 3$, simplifying to $y = \frac { t } { 6 } + 1 + 1 - 27$. Differentiating $y$ with respect to $t$ gives $\frac { d y } { d t } = \frac { 1 } { 6 }$, since the derivative of a constant is 0 and the derivative of $\frac { t } { 6 }$ with respect to $t$ is $\frac { 1 } { 6 }$.

If Y = U + 1 - 81/381 / 381/3 And U =

If Y = U + 1 - $81 / 3$ And U =