Find the given derivative by finding the first few derivatives and observing the pattern that occurs? $(\frac{d^{107}}{{d x}^{107}}) \cdot (sin (x))$ $((d^107)/(dx^107))*(sin(x))$

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Find the given derivative by finding the first few derivatives and observing the pattern that occurs? $(\frac{d^{107}}{{d x}^{107}}) \cdot (sin (x))$ $((d^107)/(dx^107))*(sin(x))$

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Answer 1 · 2018-03-16T19:51:31

$- cos x$ $-cos x$

Explanation:

$\frac{d}{d x} sin x = cos x$ $d/dx sin x = cos x$
$\frac{d^{2}}{{d x}^{2}} sin x = - sin x$ $d^2/dx^2 sin x= - sin x$
$\frac{d^{3}}{{d x}^{3}} sin x = - cos x$ $d^3/dx^3 sin x= - cos x$
$\frac{d^{4}}{{d x}^{4}} sin x = sin x$ $d^4/dx^4 sin x= sin x$

So, every fourth derivative of $sin x$ $sin x$ is back to $sin x$ $sin x$ . Thus the 104th derivative of $sin x$ $sin x$ is also $sin x$ $sin x$ , and the 107th derivative is the same as the third.

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Find the given derivative by finding the first few derivatives and observing the pattern that occurs? $(\frac{d^{107}}{{d x}^{107}}) \cdot (sin (x))$ $((d^107)/(dx^107))*(sin(x))$

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Explanation:

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Find the given derivative by finding the first few derivatives and observing the pattern that occurs? ((d^107)/(dx^107))*(sin(x))(d107dx107)⋅(sin(x))((d^107)/(dx^107))*(sin(x))

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Explanation:

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Find the given derivative by finding the first few derivatives and observing the pattern that occurs? $(\frac{d^{107}}{{d x}^{107}}) \cdot (sin (x))$ $((d^107)/(dx^107))*(sin(x))$