Find the derivative of the function. $f ( \theta ) = \frac { 7 } { 5 } \sin ^ { 2 } 2 \theta$
A) $f ^ { t } ( \theta ) = - \frac { 28 \sin 2 \theta \cos 2 \theta } { 5 }$
B) $f ^ {t } ( \theta ) = \frac { 28 \cos 2 \theta } { 5 }$
C) $f ^ { t } ( \theta ) = \frac { 28 \sin 2 \theta \cos 2 \theta } { 5 }$
D) $f ^ {t } ( \theta ) = \frac { 7 \sin 2 \theta \cos 2 \theta } { 5 }$
E) $f ^ { t } ( \theta ) = \frac { 28 \sin 2 \theta } { 5 }$

Question

Quizplus · Accepted Answer

Use the chain rule, product rule and power rule.
$$
\begin{aligned} f ^ { t } ( 	heta ) =& \frac { d } { d 	heta } \left( \frac { 7 } { 5 } \sin ^ { 2 } 2 	heta ight) \ =& \frac { 7 } { 5 } \cdot 2 \sin 2 	heta \cdot \frac { d } { d 	heta } ( \sin 2 	heta ) \ =& \frac { 14 } { 5 } \sin 2 	heta \cos 2 	heta \cdot 2\ =& \frac { 28 \sin 2 	heta \cos 2 	heta } { 5 } \end{aligned}
$$

Find the Derivative of the Function f(θ)=75sin⁡22θf ( \theta ) = \frac { 7 } { 5 } \sin ^ { 2 } 2 \thetaf(θ)=57​sin22θ

Find the Derivative of the Function $f ( \theta ) = \frac { 7 } { 5 } \sin ^ { 2 } 2 \theta$