Find the Derivative - d/dy 2cos(2y)

Problem

d()/d(y)*2*cos(2*y)

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

d()/d(y)*2*cos(2*y)=2d(cos(2*y))/d(y)

2. Apply the chain rule to the cosine function, where the outer function is cos(u) and the inner function is u=2*y

d(cos(2*y))/d(y)=−sin(2*y)⋅(d(2)*y)/d(y)

3. Differentiate the inner function 2*y with respect to y

(d(2)*y)/d(y)=2

4. Substitute the derivative of the inner function back into the expression.

2⋅(−sin(2*y)⋅2)

5. Simplify the expression by multiplying the constants.

−4*sin(2*y)

Final Answer

d()/d(y)*2*cos(2*y)=−4*sin(2*y)

Want more problems? Check here!