Find the derivative of y=4sinx−2cosx
y'=4cosx+2sinx
To find the derivative of y = 4sin(x) - 2cos(x), we can use the rules of differentiation. Before proceeding, let's briefly review the derivative formulas for the standard trigonometric functions:
- d/dx(sin(x)) = cos(x)
- d/dx(cos(x)) = -sin(x)
Now let's differentiate each term separately and then combine the results:
Term 1 (4sin(x)):
Using the formula for the derivative of sin(x), we have d/dx(4sin(x)) = 4 * cos(x) = 4cos(x).
Term 2 (-2cos(x)):
Using the formula for the derivative of cos(x), we have d/dx(-2cos(x)) = -2 * (-sin(x)) = 2sin(x).
Summing the derivatives of each term, we get:
dy/dx = 4cos(x) + 2sin(x)
Therefore, the derivative of y with respect to x is given by dy/dx = 4cos(x) + 2sin(x).