If y=5 cos x-3 sin x,then frac{d^2 y}{d x^2}= | vedclass

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Question

(C) Given $y = 5 \cos x - 3 \sin x$. First,differentiate with respect to $x$: $\frac{d y}{d x} = \frac{d}{d x}(5 \cos x - 3 \sin x) = -5 \sin x - 3 \c

Vedclass · Accepted Answer

$-y$

Vedclass · Answer

(C) Given $y = 5 \cos x - 3 \sin x$. First,differentiate with respect to $x$: $\frac{d y}{d x} = \frac{d}{d x}(5 \cos x - 3 \sin x) = -5 \sin x - 3 \cos x$. Now,differentiate again with respect to $x$ to find the second derivative: $\frac{d^2 y}{d x^2} = \frac{d}{d x}(-5 \sin x - 3 \cos x) = -5 \cos x - 3(-\sin x) = -5 \cos x + 3 \sin x$. Factor out $-1$: $\frac{d^2 y}{d x^2} = -(5 \cos x - 3 \sin x)$. Since $y = 5 \cos x - 3 \sin x$,we have: $\frac{d^2 y}{d x^2} = -y$. Thus,the correct option is $C$.

If $y=5 \cos x-3 \sin x$,then $\frac{d^2 y}{d x^2}=$ . . . . . . .

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