Find the derivative of f(x)= sin (7x)· sin (8x).
A) $7 \cos ( 8 x ) \sin ( 7 x ) - 8 \cos ( 7 x ) \sin ( 8 x )$
B) $7 \cos ( 8 x ) \sin ( 7 x ) + 8 \cos ( 7 x ) \sin ( 8 x )$
C) $8 \cos ( 8 x ) \sin ( 7 x ) - 7 \cos ( 7 x ) \sin ( 8 x )$
D) $8 \cos ( 8 x ) \sin ( 7 x ) + 7 \cos ( 7 x ) \sin ( 8 x )$

Question

Quizplus · Accepted Answer

To find the derivative of $f(x) = \sin(7x) \cdot \sin(8x)$, we use the product rule for differentiation, which is $(uv)' = u'v + uv'$. Let $u = \sin(7x)$ and $v = \sin(8x)$. Then, $u' = 7\cos(7x)$ and $v' = 8\cos(8x)$. Applying the product rule, we get $f'(x) = 7\cos(7x) \cdot \sin(8x) + \sin(7x) \cdot 8\cos(8x)$, which matches option D.

Find the Derivative of F(x)= Sin (7x)· Sin (8x) 7cos⁡(8x)sin⁡(7x)−8cos⁡(7x)sin⁡(8x)7 \cos ( 8 x ) \sin ( 7 x ) - 8 \cos ( 7 x ) \sin ( 8 x )7cos(8x)sin(7x)−8cos(7x)sin(8x)

Find the Derivative of F(x)= Sin (7x)· Sin (8x) $7 \cos ( 8 x ) \sin ( 7 x ) - 8 \cos ( 7 x ) \sin ( 8 x )$