Question

Differentiate y=3xcosx+sinx

Answer 1

Explanation:

To differentiate y = 3x cos(x) + sin(x), we can use the product rule and the chain rule.

Let's start by differentiating the first term, 3x cos(x), using the product rule:

d/dx (3x cos(x)) = 3 cos(x) - 3x sin(x)

Next, we can differentiate the second term, sin(x), using the chain rule:

d/dx (sin(x)) = cos(x)

Putting it all together, we get:

dy/dx = 3 cos(x) - 3x sin(x) + cos(x)

Simplifying the expression, we get:

dy/dx = (4cos(x)) - (3xsin(x))

Therefore, the derivative of y = 3x cos(x) + sin(x) is dy/dx = 4cos(x) - 3xsin(x).