How do you compute the 200th derivative of f(x)=sin(2x)?

aqkuax86xp0o

aqkuax86xp0o

Answered question

2023-02-17

How to compute the 200th derivative of f ( x ) = sin ( 2 x ) ?

Answer & Explanation

evefaustovefemqp5

evefaustovefemqp5

Beginner2023-02-18Added 4 answers

Step 1
f ( x ) = sin ( 2 x )
d d x f ( x ) = 2 cos ( 2 x )
d 2 d x 2 f ( x ) = - 2 2 sin ( 2 x )
d 3 d x 3 f ( x ) = - 2 3 cos ( 2 x )
d 4 d x 4 f ( x ) = 2 4 sin ( 2 x )
Step 2
This means that differentiating f(x) four times yields the same function with a multiplier of four.
Step 3
Differentiating 200 times is the same as repeating the above 50 times, and therefore
d 200 d x 200 f ( x ) = ( 2 4 ) 50 sin ( 2 x ) = 2 200 sin ( 2 x )

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