Question

What is the derivative of (x+1)sinx?

A. (x+1)tanxsinx
B. sinxsinx+(x+1)cosx
C. (x+2)cosx
D. (x+1)cosx

Answer 1

The derivative of the function (x+1)sin(x) is obtained using the product rule and the correct answer is D. (x+1)cos(x).

Step-by-step explanation:

The student is asking about the derivative of the function (x+1)sin(x). To find the derivative, we must apply the product rule, which states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. Using this rule:

• Derivative of the first function (x+1) is 1.
• Keep the second function (sin(x)) as is.
• Keep the first function (x+1) as is and take the derivative of the second function (sin(x)), which is cos(x).

Putting it all together, the derivative is:

(1)(sin(x)) + (x+1)(cos(x))

This simplifies to sin(x) + (x+1)cos(x). Therefore, the correct answer is D. (x+1)cos(x).