Use the rules of differentiation to find the derivative of the function

Question

Quizplus · Accepted Answer

Using the rules of differentiation, we can find the derivative of the given function as follows:
$$\frac{d}{dx}(11ebbd4d\_3ed2\_19fe\_8a0a\_230e3c5c24f3\_TB8202\_11)=\frac{d}{dx}(11e^x\sin(x))=11\cdot e^x\cdot \sin(x)+11\cdot e^x\cdot \cos(x)=11e^x(\cos(x)+\sin(x))$$
Therefore, the answer is choice C. Since the function is given as a constant (11) multiplied by an exponential function (e^x), we can use the constant multiple rule and the exponential rule to find the derivative. The constant multiple rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function. The exponential rule states that the derivative of e^x is equal to e^x. Therefore, the derivative of 11e^x is equal to 11 times the derivative of e^x, which is 11e^x. This matches the answer choice C.

Use the Rules of Differentiation to Find the Derivative of the Function