Find the 2nd Derivative cos(2x)

Problem

d^2(cos(2*x))/(d(x)^2)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=cos(2*x)

2. Apply the chain rule to find the first derivative, where the derivative of cos(u) is −sin(u) and the derivative of the inner function 2*x is 2

d(cos(2*x))/d(x)=−2*sin(2*x)

3. Differentiate again by applying the chain rule to the first derivative, where the derivative of sin(u) is cos(u) and the derivative of the inner function 2*x is 2

d^2(cos(2*x))/(d(x)^2)=(d(−)*2*sin(2*x))/d(x)

4. Simplify the expression by multiplying the constants −2 and 2

d^2(cos(2*x))/(d(x)^2)=−4*cos(2*x)

Final Answer

d^2(cos(2*x))/(d(x)^2)=−4*cos(2*x)

Want more problems? Check here!