Calc high d/dx problem

Calculus Level 2

If f ( x ) = 2 sin ⁡ ( x 2 ) cos ⁡ ( x 2 ) f(x) = 2 \sin \left(\frac x2\right) \cos \left(\frac x2\right) , what is the 1000th derivative of f ( x ) f(x) ?

sin ⁡ x \sin x 0 0 − sin ⁡ x -\sin x cos ⁡ x \cos x

Ahmed Mahmoud by Ahmed Mahmoud , 20, Egypt

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1 solution

Steven Chase
Apr 22, 2019

2 s i n ( x / 2 ) c o s ( x / 2 ) = s i n ( x ) 2 \, sin(x/2) \, cos(x/2) = sin(x)

Taking four derivatives gets us back to s i n ( x ) sin(x) . Since 1000 1000 is an even multiple of 4 4 , we end up with s i n ( x ) sin(x)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Sir, try this .
Btw, I think that your new problem is really tedious to solve by hand, as compared to the original problem ;)

Aaghaz Mahajan - 2 years, 1 month ago

bah youpi alors

Melvin Frayon - 2 years, 1 month ago

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