If $f ( x ) = ( 7 x + \sin x ) ^ { e }$
, then $f ^ { \prime } ( x ) = ( 7 + \cos x ) \cdot \ln ( 7 x + \sin x ) \cdot ( 7 x + \sin x ) ^ { e }$ .

Question

If $f ( x ) = ( 7 x + \sin x ) ^ { e }$ , then $f ^ { \prime } ( x ) = ( 7 + \cos x ) \cdot \ln ( 7 x + \sin x ) \cdot ( 7 x + \sin x ) ^ { e }$ .

Quizplus · Accepted Answer

The correct derivative of $f(x) = (7x + \sin x)^e$ involves applying the chain rule and the power rule correctly, but the given expression misses the factor of $e$ from the exponent in the derivative of the power function. The correct derivative should include $e \cdot (7x + \sin x)^{e-1}$ as part of the expression, along with the derivative of the inside function, $7 + \cos x$, and the chain rule application would also multiply by the original function's exponent, $e$, not just by $\ln(7x + \sin x)$.

If f(x)=(7x+sin⁡x)ef ( x ) = ( 7 x + \sin x ) ^ { e }f(x)=(7x+sinx)e

If $f ( x ) = ( 7 x + \sin x ) ^ { e }$