Let f(x)=sin(x)x^(-2). Find f^(')(x). Choose 1 answer: (A) (cos(x))/(x^(2))-(2sin(x))/(x^(3)) (B) (cos(x))/(x^(2))-(2sin(x))/(x) (C) (sin(x))/(x^(2))-(2cos(x))/(x) (D) (sin(x))/(x^(2))-(2cos(x))/(x^(3))

Apply Product Rule: Use the product rule for differentiation: (d/dx)[u(x)v(x)] = u'(x)v(x) + u(x)v'(x), where u(x) = sin(x) and v(x) = x^(-2).Differentiate sin(x): Differentiate u(x) = sin(x). The derivative of sin(x) with respect to x is cos(x), so u'(x) = cos(x).Differentiate x^(-2): Differentiate v(x) = x^(-2). The derivative of x^(-2) with respect to x is -2x^(-3), so v'(x) = -2x^(-3).Apply Product Rule: Apply the product rule: f'(x) = cos(x)*x^(-2) + sin(x)*(-2x^(-3)).Simplify Expression: Simplify the expression: f'(x) = (cos(x)/x^2) - (2sin(x)/x^3).

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Let
f(x)=sin(x)x^(-2).
Find
f^(')(x).
Choose 1 answer:
(A)
(cos(x))/(x^(2))-(2sin(x))/(x^(3))
(B)
(cos(x))/(x^(2))-(2sin(x))/(x)
(C)
(sin(x))/(x^(2))-(2cos(x))/(x)
(D)
(sin(x))/(x^(2))-(2cos(x))/(x^(3))

Let $f(x)=\sin (x) x^{-2}$ . $\newline$ Find $f^{\prime}(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\cos (x)}{x^{2}}-\frac{2 \sin (x)}{x^{3}}$ $\newline$ (B) $\frac{\cos (x)}{x^{2}}-\frac{2 \sin (x)}{x}$ $\newline$ (C) $\frac{\sin (x)}{x^{2}}-\frac{2 \cos (x)}{x}$ $\newline$ (D) $\frac{\sin (x)}{x^{2}}-\frac{2 \cos (x)}{x^{3}}$

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Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Let

f(x)=\sin (x) x^{-2}

\newline

Find

f^{\prime}(x)

\newline

Choose

1

answer:

\newline

(A)

\frac{\cos (x)}{x^{2}}-\frac{2 \sin (x)}{x^{3}}

\newline

(B)

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

\newline

(C)

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

\newline

(D)

\frac{\sin (x)}{x^{2}}-\frac{2 \cos (x)}{x^{3}}

Apply Product Rule: Use the product rule for differentiation: $(\frac{d}{dx})[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$ , where $u(x) = \sin(x)$ and $v(x) = x^{-2}$ .
Differentiate $\sin(x)$ : Differentiate $u(x) = \sin(x)$ . The derivative of $\sin(x)$ with respect to $x$ is $\cos(x)$ , so $u'(x) = \cos(x)$ .
Differentiate $x^{-2}$ : Differentiate $v(x) = x^{-2}$ . The derivative of $x^{-2}$ with respect to $x$ is $-2x^{-3}$ , so $v'(x) = -2x^{-3}$ .
Apply Product Rule: Apply the product rule: $f'(x) = \cos(x)\cdot x^{-2} + \sin(x)\cdot (-2x^{-3})$ .
Simplify Expression: Simplify the expression: $f'(x) = \frac{\cos(x)}{x^2} - \frac{2\sin(x)}{x^3}$ .