$\text { Find the second derivative of the function } f ( x ) = \sin 5 x ^ { 6 } \text {. }$
A) $f ^ { tt } ( x ) = 30 x ^ { 4 } \cos 5 x ^ { 6 } + 30 x ^ { 10 } \sin 5 x ^ { 6 }$
B) $f ^ { tt } ( x ) = 30 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$
C) $f ^ { tt } ( x ) = 180 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$
D) $f ^ { tt } ( x ) = 150 x ^ { 4 } \cos 5 x ^ { 6 } + 900 x ^ { 10 } \sin 5 x ^ { 6 }$
E) $f ^ { tt } ( x ) = 150 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$

Question

$\text { Find the second derivative of the function } f ( x ) = \sin 5 x ^ { 6 } \text {. }$ 
A) $f ^ { tt } ( x ) = 30 x ^ { 4 } \cos 5 x ^ { 6 } + 30 x ^ { 10 } \sin 5 x ^ { 6 }$
B) $f ^ { tt } ( x ) = 30 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$
C) $f ^ { tt } ( x ) = 180 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$
D) $f ^ { tt } ( x ) = 150 x ^ { 4 } \cos 5 x ^ { 6 } + 900 x ^ { 10 } \sin 5 x ^ { 6 }$
E) $f ^ { tt } ( x ) = 150 x ^ { 4 } \cos 5 x ^ { 6 } - 900 x ^ { 10 } \sin 5 x ^ { 6 }$

Quizplus · Accepted Answer

To find the second derivative of $f(x) = \sin(5x^6)$, we first find the first derivative using the chain rule: $f'(x) = 30x^5\cos(5x^6)$. Then, applying the product and chain rules for the second derivative, we get $f''(x) = 150x^4\cos(5x^6) - 900x^{10}\sin(5x^6)$.

Find the second derivative of the function f(x)=sin⁡5x6. \text { Find the second derivative of the function } f ( x ) = \sin 5 x ^ { 6 } \text {. } Find the second derivative of the function f(x)=sin5x6.

$\text { Find the second derivative of the function } f ( x ) = \sin 5 x ^ { 6 } \text {. }$