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Alessandro
Mathematics
14 May, 05:22
Find the 57th derivative of y = cos (7x).
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Madelynn Jones
14 May, 05:23
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y = cos (7x)
First derivative = - 7sin (7x)
Second derivative = - (7^2) cos (7x)
3rd derivative = (7^3) sin (7x)
4th derivative = (7^4) cos (7x)
5th derivative = - (7^5) sin (7x)
6th derivative = - (7^6) cos (7x)
nth derivative?
Analysis and conclusion
If n is multiple of 4 or a number before a multiple of 8 the sign is positive
If n is one or two numbers after a multiple of 4 the sign is negative.
7 is raised to exponent n
if n is odd the function is sin (7x), if n is even the function is cos (7x)
n = 57 = > odd, and it is a number after 56 which is a multiple of 4 = > negative sign
Therefore, the 57th derivative = - (7^57) sin (7x)
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