$$\text { Find the derivative of the function } f ( t ) = 15 t ^ { 3 } + 6 \sec ( t ) \text {. }$$
A) $f ^ { t} ( t ) = 45 t ^ { 2 } + 6 \sec ( t ) \tan ( t )$
B) $f ^ { t } ( t ) = 3 t ^ { 2 } + 6 \sec ^ { 2 } ( t )$
C) $f ^ {t} ( t ) = 45 t ^ { 2 } + 6 \tan ( t )$
D) $f ^ { t } ( t ) = 3 t ^ { 2 } + 6 \sec ( t ) \tan ( t )$
E) $f ^ { t} ( t ) = 45 t ^ { 2 } - 6 \sec ( t ) \tan ( t )$

Question

$$\text { Find the derivative of the function } f ( t ) = 15 t ^ { 3 } + 6 \sec ( t ) \text {. }$$ 
A) $f ^ { t} ( t ) = 45 t ^ { 2 } + 6 \sec ( t ) \tan ( t )$
B) $f ^ { t } ( t ) = 3 t ^ { 2 } + 6 \sec ^ { 2 } ( t )$
C) $f ^ {t} ( t ) = 45 t ^ { 2 } + 6 \tan ( t )$
D) $f ^ { t } ( t ) = 3 t ^ { 2 } + 6 \sec ( t ) \tan ( t )$
E) $f ^ { t} ( t ) = 45 t ^ { 2 } - 6 \sec ( t ) \tan ( t )$

Quizplus · Accepted Answer

The derivative of $15t^3$ is $45t^2$ using the power rule, and the derivative of $6\sec(t)$ is $6\sec(t)\tan(t)$ using the chain rule.

Find the derivative of the function f(t)=15t3+6sec⁡(t). \text { Find the derivative of the function } f ( t ) = 15 t ^ { 3 } + 6 \sec ( t ) \text {. } Find the derivative of the function f(t)=15t3+6sec(t).

$\text { Find the derivative of the function } f ( t ) = 15 t ^ { 3 } + 6 \sec ( t ) \text {. }$