Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

Since is constant with respect to , the derivative of with respect to is .

Move to the left of .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Multiply by .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

Since is constant with respect to , the derivative of with respect to is .

Multiply by .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Multiply by .

Differentiate using the Power Rule which states that is where .

Multiply by .

The 4th derivative of with respect to is .

Find the 3rd Derivative f(x)=sin(2x)