Find $f ^ { \prime } ( t )$ if $f ( t ) = t ^ { 10 } 10 ^ { 3 t }$ .
A) $f ^ { \prime } ( t ) = 10 t ^ { 9 } 10 ^ { 3 t } + 3 t ^ { 10 } 10 ^ { 3 t }$
B) $f ^ { \prime } ( t ) = 10 t ^ { 9 } 10 ^ { 3 t } + 10 ^ { 3 t - 1 }$
C) $f ^ { \prime } ( t ) = 10 t ^ { 9 } 10 ^ { 3 t } + 3 \ln ( 10 ) t ^ { 10 } 10 ^ { 3 t }$
D) $f ^ { \prime } ( t ) = 10 t ^ { 9 } 10 ^ { 3 t } + 30 t ^ { 10 } 10 ^ { 3 t }$
E) $f ^ { \prime } ( t ) = 10 t ^ { 9 } 30 ^ { 3 t - 1 }$

Question

Quizplus · Accepted Answer

The derivative is found using the product rule and chain rule. The derivative of $t^{10}$ is $10t^9$, and the derivative of $10^{3t}$ is $3\ln(10) \cdot 10^{3t}$.

Find f′(t)f ^ { \prime } ( t )f′(t) If f(t)=t10103tf ( t ) = t ^ { 10 } 10 ^ { 3 t }f(t)=t10103t

Find $f ^ { \prime } ( t )$ If $f ( t ) = t ^ { 10 } 10 ^ { 3 t }$