$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$
A) $H ^ { t } ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } - 25 t ^ { 4 }$
B) $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } + 36 t ^ { 4 }$
C) $H ^ { t} ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } + 25 t ^ { 4 }$
D) $H ^ {t } ( s ) = 11 t ^ { 10 } - 36 t ^ { 5 } - 25 t ^ { 4 }$
E) $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } - 6 t ^ { 4 }$

Question

$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$ 
A) $H ^ { t } ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } - 25 t ^ { 4 }$
B) $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } + 36 t ^ { 4 }$
C) $H ^ { t} ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } + 25 t ^ { 4 }$
D) $H ^ {t } ( s ) = 11 t ^ { 10 } - 36 t ^ { 5 } - 25 t ^ { 4 }$
E) $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } - 6 t ^ { 4 }$

Quizplus · Accepted Answer

To find the derivative of $H(t) = (t^6 - 5)(t^5 + 6)$, first apply the product rule: $\frac{d}{dt}[u \cdot v] = u' \cdot v + u \cdot v'$, where $u = t^6 - 5$ and $v = t^5 + 6$. The derivatives are $u' = 6t^5$ and $v' = 5t^4$. Thus, $H'(t) = 6t^5(t^5 + 6) + (t^6 - 5)5t^4 = 6t^{10} + 36t^5 + 5t^{10} - 25t^4 = 11t^{10} + 36t^5 - 25t^4$.

Find the derivative of the algebraic function H(t)=(t6−5)(t5+6)\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right) Find the derivative of the algebraic function H(t)=(t6−5)(t5+6)

$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$