Find the 2nd Derivative sin(2x)

Problem

d2(sin(2*x))/(d(x)2)

Solution

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

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

3. Calculate the first derivative:

d(sin(2*x))/d(x)=cos(2*x)⋅2

4. Simplify the first derivative expression:

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

5. Differentiate again by applying the chain rule to the first derivative to find the second derivative.

6. Calculate the second derivative:

d2(sin(2*x))/(d(x)2)=2⋅(−sin(2*x)⋅2)

7. Simplify the final expression by multiplying the constants:

d2(sin(2*x))/(d(x)2)=−4*sin(2*x)

Final Answer

d2(sin(2*x))/(d(x)2)=−4*sin(2*x)

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