Differentiate the given function. $g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }$
A) $50 \sin ^ { 9 } t \cdot \cos t - 60 \sin ^ { 9 } t \cdot \cos t$
B) $- 5 \cos ^ { 10 } t + 6 \cos t ^ { 10 }$
C) $5 \cos ^ { 10 } t - 6 \cos ^ { 10 }$
D) $50 \sin ^ { 9 } t \cdot \cos t - 60 t ^ { 9 } \cos t ^ { 10 }$

Question

Quizplus · Accepted Answer

The differentiation of $g(t) = 5\sin^{10}t - 6\sin t^{10}$ using the chain rule gives $50\sin^{9}t \cdot \cos t$ for the first term and $-60t^{9}\cos t^{10}$ for the second term, leading to the correct answer $50\sin^{9}t \cdot \cos t - 60t^{9}\cos t^{10}$.

Differentiate the Given Function g(t)=5sin⁡10t−6sin⁡t10g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }g(t)=5sin10t−6sint10

Differentiate the Given Function $g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }$