exercises 3.5 derivatives of trigonometric functions\nscore: 32/37 answered: 16/18\nquestion 17\nlet (…
exercises 3.5 derivatives of trigonometric functions\nscore: 32/37 answered: 16/18\nquestion 17\nlet ( f(x)=cos (x) ), find each of the following:\nfind the second derivative, ( f^{prime prime}(x)=)\nfind the third derivative, ( f^{prime prime prime}(x)=)\nfind the fourth derivative, ( f^{prime prime prime prime}(x)=)\nquestion help: video message instructor\nsubmit question jump to answer
Answer
Explanation:
Step1: Find the first derivative
The derivative of ( \cos(x) ) is ( -\sin(x) ), so ( f'(x)=-\sin(x) ).
Step2: Find the second derivative
The derivative of ( -\sin(x) ) is ( -\cos(x) ), so ( f''(x)=-\cos(x) ).
Step3: Find the third derivative
The derivative of ( -\cos(x) ) is ( \sin(x) ), so ( f'''(x)=\sin(x) ).
Step4: Find the fourth derivative
The derivative of ( \sin(x) ) is ( \cos(x) ), so ( f''''(x)=\cos(x) ).
Answer:
( f''(x)=-\cos(x) ) ( f'''(x)=\sin(x) ) ( f''''(x)=\cos(x) )