Let f(x) = sinx Find D^555f
I am not familiar with the notation and I'm pretty sure it deals with implicit differentiation. Any help is appreciated. Thanks
I am not familiar with the notation and I'm pretty sure it deals with implicit differentiation. Any help is appreciated. Thanks
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The differentiation is explicit. "D^555" just refers to the 555th derivative. You might find it more familiar in the form
d^(555)f/dx^(555)
At any rate, note that derivatives cycle.
f(x) = sin(x), f '(x) = cos(x), f ''(x) = -sin(x), f '''(x) = -cos(x), and finally f ''''(x) = sin(x) = f(x).
Since 555 = 138(4) + 3, that is the remainder of 555 when divided by 4 is 3,
D^(555) sin(x) = f '''(x) = -cos(x).
d^(555)f/dx^(555)
At any rate, note that derivatives cycle.
f(x) = sin(x), f '(x) = cos(x), f ''(x) = -sin(x), f '''(x) = -cos(x), and finally f ''''(x) = sin(x) = f(x).
Since 555 = 138(4) + 3, that is the remainder of 555 when divided by 4 is 3,
D^(555) sin(x) = f '''(x) = -cos(x).