Math, asked by salmaprodduturu3957, 7 months ago

Find the nth derivative of (cosx)^9

Answers

Answered by brrosiis
1

Answer:

y ' = 9 * cos^8(x) * (-sin x) = -9* cos^8(x)*sin(x)

y'' = -9*cos^8(x) * cos(x) + 72*cos^7(x)*sin^2(x)

= 72*cos^7(x)*sin^2(x) - 9*cos^9(x) <-------------- 1st term: 9 * 8 = 72 ; the exponents add up to 9

[done with calculator]

y''' = 255*cos^8(x)*sin(x) - 504*cos^6(x)*sin^3(x) <--- 2nd term: 7 * 72 = 504; exponents add up to 9

[done with calculator]

y(4) = 3024* cos^5(x)*sin^4(x) - 3122 * cos^7(x)*sin^2(x) + 255*cos^9(x) <--- 504*6 = 3024; expo. add up to 9

So in the next derivative it shall be 3024*5 = 15120*cos^4(x)*sin^5(x)

you then need to find a pattern for the other terms in the series

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