Calculus #4: $\frac{{d}^{4n}(\cos{(x))}}{{dx}^{4n}}$

Calculus Level 2

Find the value of $\dfrac{d^{4n}}{dx^{4n}}\cos (x)$ , where $n$ is a positive integer.

None of these.

\cos(x)

-\sin(x)

-\cos(x)

Varies.

\sin(x)

1 solution

Edwin Gray
Sep 5, 2018

Defining f(x) = cos(x), we have f'(x) = -sin(x), f''(x) = - cos(x), f'''(x) = +sin(x), f''''(x) = cos(x). The sequence repeats indefinitely, so that every fourth derivative equals cos(x). Ed Gray

Calculus #4: d 4 n ( cos ⁡ ( x ) ) d x 4 n \frac{{d}^{4n}(\cos{(x))}}{{dx}^{4n}} d x 4 n d 4 n ( cos ( x ) ) ​

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Calculus #4: $\frac{{d}^{4n}(\cos{(x))}}{{dx}^{4n}}$