Find the 4th Derivative f(x)=sin(x)

Problem

d4(sin(x))/(d(x)4)

Solution

1. Find the first derivative by applying the derivative rule for the sine function.

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

2. Find the second derivative by differentiating the first derivative.

d(cos(x))/d(x)=−sin(x)

3. Find the third derivative by differentiating the second derivative.

(d(−)*sin(x))/d(x)=−cos(x)

4. Find the fourth derivative by differentiating the third derivative.

(d(−)*cos(x))/d(x)=sin(x)

Final Answer

d4(sin(x))/(d(x)4)=sin(x)

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