Let y=sqrtxcos(x). Find (dy)/(dx). Choose 1 answer: (A) -(1)/(sqrtx)+sin(x) (B) (cos(x))/(2sqrtx)-sqrtxsin(x) (C) -(sin(x))/(sqrtx) (D) -2sqrtxcos(x)-sqrtxsin(x)

Define u and v: Using the product rule, which states that (d/dx)[u(x)v(x)] = u'(x)v(x) + u(x)v'(x), let's differentiate y. Let u = sqrt(x) and v = cos(x).Differentiate u: Differentiate u = sqrt(x) with respect to x to get u'. u' = (1/2)x^(-1/2)Differentiate v: Differentiate v = cos(x) with respect to x to get v'. v' = -sin(x)Apply product rule: Now plug u', v, u, and v' into the product rule formula. (dy/dx) = (1/2)x^(-1/2)cos(x) + sqrt(x)(-sin(x))Simplify expression: Simplify the expression. (dy/dx) = (cos(x))/(2sqrt(x)) - sqrt(x)sin(x)

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Let
y=sqrtxcos(x).
Find
(dy)/(dx).
Choose 1 answer:
(A)
-(1)/(sqrtx)+sin(x)
(B)
(cos(x))/(2sqrtx)-sqrtxsin(x)
(C)
-(sin(x))/(sqrtx)
(D)
-2sqrtxcos(x)-sqrtxsin(x)

Let $y=\sqrt{x} \cos (x)$ . $\newline$ Find $\frac{d y}{d x}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{1}{\sqrt{x}}+\sin (x)$ $\newline$ (B) $\frac{\cos (x)}{2 \sqrt{x}}-\sqrt{x} \sin (x)$ $\newline$ (C) $-\frac{\sin (x)}{\sqrt{x}}$ $\newline$ (D) $-2 \sqrt{x} \cos (x)-\sqrt{x} \sin (x)$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Let

y=\sqrt{x} \cos (x)

\newline

Find

\frac{d y}{d x}

\newline

Choose

1

answer:

\newline

(A)

-\frac{1}{\sqrt{x}}+\sin (x)

\newline

(B)

\frac{\cos (x)}{2 \sqrt{x}}-\sqrt{x} \sin (x)

\newline

(C)

-\frac{\sin (x)}{\sqrt{x}}

\newline

(D)

-2 \sqrt{x} \cos (x)-\sqrt{x} \sin (x)

Define $u$ and $v$ : Using the product rule, which states that $\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$ , let's differentiate $y$ . $\newline$ Let $u = \sqrt{x}$ and $v = \cos(x)$ .
Differentiate $u$ : Differentiate $u = \sqrt{x}$ with respect to $x$ to get $u'$ . $\newline$ $u' = (\frac{1}{2})x^{(-\frac{1}{2})}$
Differentiate $v$ : Differentiate $v = \cos(x)$ with respect to $x$ to get $v'$ . $\newline$ $v' = -\sin(x)$
Apply product rule: Now plug $u'$ , $v$ , $u$ , and $v'$ into the product rule formula. $\newline$ $(dy/dx) = (1/2)x^{(-1/2)}\cos(x) + \sqrt{x}(-\sin(x))$
Simplify expression: Simplify the expression. $\frac{dy}{dx} = \frac{\cos(x)}{2\sqrt{x}} - \sqrt{x}\sin(x)$