[Urgent] Differentiation (1 Viewer)

[mathyics]

Find the first, second, third, fourth, fifth derivatives of the function y = sin 3x.

Find the rules that can help to find the 50th derivative of the function.

It's urgent! My attempt to the question: y = -a^n sin ax for even
y = a^n cos ax for odd

Plz show steps so that i can follow, cheers

 

[Slowness]

I got

y=sin3x
y'=3cos3x
y''=-9sin3x
y'''=-27cos3x
y''''=81sin3x
y'''''=243 cos3x

Using your one, for y'''

We would go 3^3 Cos3x which won't work out because you are supposed to have a negative.

I can't think of a general solution but still thinking ....

 

[mathyics]

I got

y=sin3x
y'=3cos3x
y''=-9sin3x
y'''=-27cos3x
y''''=81sin3x
y'''''=243 cos3x

Using your one, for y'''

We would go 3^3 Cos3x which won't work out because you are supposed to have a negative.

I can't think of a general solution but still thinking ....



EDIT: What topic is this?? It could possibly be related to Binomial

This topic i think is differentiation on trigonometry function. Also this would be the exam question and the teacher has only told us just before the end of lesson so i really need help on this.

Also is it even possible to have a general formula for this? i asked a friend and he said there will be three rules

 

[mathyics]

sorry it should be the 50th derivative

 

[Carrotsticks]

sorry, but i dont think there's a set method. You're gonna have to use logic and pattern-finding skills to do this. This is a most unusual question that will certainly NOT be in the HSC exam.

 

[Carrotsticks]

 

[Carrotsticks]

 

[Carrotsticks]

 

[mathyics]

i dont think that equation works for 3 (odd):

(-1)^3-1 * 3^3 cos3x
= 1 * 27 cos 3x
= 27 cox 3x

but y'''=-27cos3x

I have now found a new equation which works for 1-3 (proven) and i think it will work for odds



how do you guys think?

 

[ninetypercent]

dw about this. It is a weird question - most likely not gonna be asked!

 

[bachviete]

There are 4 general cases, you should be able to adapt it to present a solution.









As it is cyclic,

 

[Trebla]

Find the first, second, third, fourth, fifth derivatives of the function y = sin 3x.

Find the rules that can help to find the 50th derivative of the function.

It's urgent! My attempt to the question: y = -a^n sin ax for even
y = a^n cos ax for odd

Plz show steps so that i can follow, cheers

y' = 3cos 3x
y'' = - 3² sin 3x
y⁽³⁾ = - 3³ cos 3x
y⁽⁴⁾ = 3⁴ sin 3x
y⁽⁵⁾ = 3⁵ cos 3x

By inspection, for positive integers of n:
y⁽²ⁿ⁾ = (-1)ⁿ(3)²ⁿ sin 3x
and
y^(2n-1) = (-1)ⁿ⁺¹(3)^2n-1 cos 3x

 

[Trebla]

So for
y⁽²ⁿ⁾ = (-1)ⁿ(3)²ⁿ sin 3x
Let n = 25
=> y⁽⁵⁰⁾ = (-1)²⁵(3)⁵⁰ sin 3x
= - (3)⁵⁰ sin 3x
= - 717 897 987 691 852 588 770 249 sin 3x

lol