Find the derivative of
y=4sinx−2cosx
done two days ago:
http://www.jiskha.com/display.cgi?id=1465840275
To find the derivative of y = 4sin(x) - 2cos(x), we can use the rules of differentiation.
Step 1: Apply the derivative rule for sin(x).
The derivative of sin(x) is cos(x), so the derivative of 4sin(x) is 4cos(x).
Step 2: Apply the derivative rule for cos(x).
The derivative of cos(x) is -sin(x), so the derivative of -2cos(x) is 2sin(x).
Step 3: Combine the derivatives from step 1 and step 2.
The derivative of y = 4sin(x) - 2cos(x) is:
dy/dx = 4cos(x) + 2sin(x)
Therefore, the derivative of y = 4sin(x) - 2cos(x) is dy/dx = 4cos(x) + 2sin(x).
To find the derivative of the given function, y = 4sin(x) - 2cos(x), we can apply the basic rules of differentiation. Remember that the derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). The derivative of a constant term is zero.
Here are the steps to find the derivative:
Step 1: Differentiate the term 4sin(x).
The derivative of 4sin(x) is 4cos(x). We obtained this by applying the derivative of sin(x) rule, which states that the derivative of sin(x) is cos(x).
Step 2: Differentiate the term -2cos(x).
The derivative of -2cos(x) is 2sin(x). We obtained this by applying the derivative of cos(x) rule, which states that the derivative of cos(x) is -sin(x).
Step 3: Combine the derivatives.
Since we differentiated both terms separately, we can now combine the derivatives. The derivative of y = 4sin(x) - 2cos(x) would be:
dy/dx = 4cos(x) + 2sin(x)
Therefore, the derivative of y = 4sin(x) - 2cos(x) is dy/dx = 4cos(x) + 2sin(x).
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