Find the derivative of the function. $$f ( t ) = \left( 4 + 7 t ^ { 5 } \right) ^ { 8 }$$
A) $f ^ {t } ( t ) = 280 t ^ { 4 } \left( 4 + 7 t ^ { 4 } \right) ^ { 7 }$
B) $f ^ {t } ( t ) = 280 t ^ { 4 } \left( 4 + 7 t ^ { 5 } \right) ^ { 7 }$
C) $f ^ { t } ( t ) = 7 t ^ { 4 } \left( 4 + 7 t ^ { 5 } \right) ^ { 7 }$
D) $f ^ { t } ( t ) = 280 t ^ { 7 } \left( 4 + 7 t ^ { 5 } \right) ^ { 7 }$
E) $f ^ { t } ( t ) = 280 t ^ { 8 } \left( 4 + 7 t ^ { 5 } \right) ^ { 7 }$

Question

Quizplus · Accepted Answer

Using the chain rule, we get $f'(t) = 8(4+7t^5)^7 \cdot 7t^4 \cdot 35t^4 = 280t^4(4+7t^5)^7$. Therefore, the answer is $\boxed{	extbf{(B)}}$.

Find the Derivative of the Function f(t)=(4+7t5)8f ( t ) = \left( 4 + 7 t ^ { 5 } \right) ^ { 8 }f(t)=(4+7t5)8

Find the Derivative of the Function $f ( t ) = \left( 4 + 7 t ^ { 5 } \right) ^ { 8 }$