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P3 differentiation (again) watch

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1. review exercise 1 Q55

b)Given that y=xsin3x, prove that f"(x) + 9f(x) = 6cos3x

f(x) = xsin3x
f'(x) = x3cos3x +sin3x
f"(x) = -x9sin3x + 3cos3x

f"(x) + 9f(x) = 3cos3x - 9xsin3x +9xsin3x = 3cos3x not 6cos3x

Where have I gone wrong. Prob some stupid mistake, I'll rep the person who spots it first.

MB
2. (Original post by musicboy)
review exercise 1 Q55

b)Given that y=xsin3x, prove that f"(x) + 9f(x) = 6cos3x

f(x) = xsin3x
f'(x) = x3cos3x +sin3x

f'(x) is 3cos3x + sin3x

Edit: sorry.....forget that
3. (Original post by musicboy)
review exercise 1 Q55

b)Given that y=xsin3x, prove that f"(x) + 9f(x) = 6cos3x

f(x) = xsin3x
f'(x) = x3cos3x +sin3x
f"(x) = -x9sin3x + 3cos3x

f"(x) + 9f(x) = 3cos3x - 9xsin3x +9xsin3x = 3cos3x not 6cos3x

Where have I gone wrong. Prob some stupid mistake, I'll rep the person who spots it first.

MB
f(x)= xsin3x
f'(x)=3xcos3x+sin3x
f''(x)=-9xsin3x+3cos3x+3cos3x
=-9xsin3x+6cos3x

So f''(x)+9f(x)=-9xsin3x+6cos3x+9xsin3x
=6cos3x

Hope that helps.
4. f''(x) = -9x*sin3x + 3cos3x + 3cos3x
5. Thanks comrades, I'll rep you both but Bezza will have to wait a day for his (sorry)

MB
6. (Original post by musicboy)
Thanks comrades, I'll rep you both but Bezza will have to wait a day for his (sorry)

MB
Thanks, but there's no need really. Happy to help.

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