Trivial Calculus

Calculus Level 1

$f(x)= \sin(x)$ .
Find $f''(x)+2$ .

-tan(x)-2 cos(x)+2 -sin(x)+2 tan(x)-2

1 solution

Michael Huang
Dec 2, 2016

Note that for each integer $(2 + 4n)$ , where $n \in \mathbb{Z}$ , $\dfrac{d^{(2 + 4n)}}{dx}\left(\sin(x)\right) = -\sin(x)$ Since $2$ is of the form $(2 + 4(0))$ , this shows that $\dfrac{d^2}{dx}\left(\sin(x)\right) = -\sin(x)$ Thus, $f''(x) + 2 = \boxed{-\sin(x) + 2}$

Trivial Calculus

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