Answer: sinx + (x+1)cosx
Step-by-step explanation:
To find the derivative of (x+1)sinx, we can use the product rule, which is given by the formula:
[tex]\dfrac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)[/tex]
Letting f(x) = x+1 and g(x) = sinx:
Now, applying the product rule:
[tex]\dfrac{d}{dx}[(x+1)sinx] = (sinx) + (x+1)cosx[/tex]
The derivative of (x+1)sinx is sinx + (x+1)cosx.
