How do you find the 27th derivative of cosx?

Question

How do you find the 27th derivative of cosx?

1 Answer

Impact of this question

39600 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-07T01:54:33

$\frac{d^{27} y}{{d x}^{27}} = sin x$ $(d^27y)/(dx^27) = sinx$

Explanation:

Consider the following pattern.

$\frac{d}{d x} (cos x) = - sin x$ $d/dx(cosx) = -sinx$

$\frac{d}{d x} (- sin x) = - cos x$ $d/dx(-sinx) = -cosx$

$\frac{d}{d x} (- cos x) = sin x$ $d/dx(-cosx) = sinx$

$\frac{d}{d x} (sin x) = cos x$ $d/dx(sinx) = cosx$

So, after differentiating $cos x$ $cosx$ four times, you will return to $cos x$ $cosx$ !!

Make a list:

$0 . cos x$ $0. cosx$
$1 . - sin x$ $1. -sinx$
$2 . - cos x$ $2. -cosx$
$3 . sin x$ $3. sinx$
$4 . cos x$ $4. cosx$

So, whenever you have an nth derivative where $n$ $n$ is divisible by $4$ $4$ , the derivative will be equal to $cos x$ $cosx$ . The closest multiple of $4$ $4$ to $27$ $27$ is $28$ $28$ . The 28th derivative of $cos x$ $cosx$ is $cos x$ $cosx$ . Go one up in the list $(3)$ $(3)$ to find that the 27th derivative of $cos x$ $cosx$ is $sin x$ $sinx$ .

Hopefully this helps!

Science

Math

Humanities

... and beyond

How do you find the 27th derivative of cosx?

1 Answer

Explanation:

Related questions

Impact of this question