Find the first derivative of w(t) = 7 $t ^ { 2 }$

Question

Find the first derivative of w(t) = 7 $t ^ { 2 }$ - 19 $\sqrt { t }$ + 23
A) 14t - $\frac { 19 } { 2 }$ $\sqrt { t }$
B) 14t - $\frac { 19 } { 2 \sqrt { t } }$
C) $\frac { 7 } { 2 }$ t - $\frac { 19 } { 2 \sqrt { t } }$
D) $\frac { 7 } { 2 }$ t - $\frac { 19 } { 2 }$ $\sqrt { t }$

Quizplus · Accepted Answer

The first derivative of $w(t) = 7t^2 - 19\sqrt{t} + 23$ is found by applying the power rule. The derivative of $7t^2$ is $14t$, the derivative of $-19\sqrt{t}$ is $-\frac{19}{2\sqrt{t}}$ (since $\sqrt{t} = t^{\frac{1}{2}}$, its derivative is $\frac{1}{2}t^{-\frac{1}{2}}$), and the derivative of a constant (23) is 0. Therefore, the correct answer is $14t - \frac{19}{2\sqrt{t}}$.

Find the First Derivative of W(t) = 7 t2t ^ { 2 }t2