Let h(x)=sqrtxln(x). Find h^(')(x). Choose 1 answer: (A) (1)/(2sqrtx)+(1)/(x) (B) (ln(x))/(2sqrtx)+(1)/(sqrtx) (C) (1)/(2sqrtx)*(1)/(x) (D) (sqrtxln(x))/(2)+(1)/(sqrtx)

Differentiate sqrt(x): Differentiate sqrt(x) with respect to x to get (1/2)x^(-1/2). Differentiate ln(x) with respect to x to get 1/x.Differentiate ln(x): Now apply the product rule: h'(x) = (sqrt(x))'(ln(x)) + (sqrt(x))(ln(x))'. This gives us h'(x) = (1/2)x^(-1/2)ln(x) + (sqrt(x))(1/x).Apply product rule: Simplify the expression: h'(x) = (1/2)x^(-1/2)ln(x) + 1/(2sqrt(x)). Oops, there's a mistake here. The second term should be 1/(2sqrt(x)) without the ln(x).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
h(x)=sqrtxln(x).
Find
h^(')(x).
Choose 1 answer:
(A)
(1)/(2sqrtx)+(1)/(x)
(B)
(ln(x))/(2sqrtx)+(1)/(sqrtx)
(C)
(1)/(2sqrtx)*(1)/(x)
(D)
(sqrtxln(x))/(2)+(1)/(sqrtx)

Let $h(x)=\sqrt{x} \ln (x)$ . $\newline$ Find $h^{\prime}(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2 \sqrt{x}}+\frac{1}{x}$ $\newline$ (B) $\frac{\ln (x)}{2 \sqrt{x}}+\frac{1}{\sqrt{x}}$ $\newline$ (C) $\frac{1}{2 \sqrt{x}} \cdot \frac{1}{x}$ $\newline$ (D) $\frac{\sqrt{x} \ln (x)}{2}+\frac{1}{\sqrt{x}}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Let

h(x)=\sqrt{x} \ln (x)

\newline

Find

h^{\prime}(x)

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2 \sqrt{x}}+\frac{1}{x}

\newline

(B)

\frac{\ln (x)}{2 \sqrt{x}}+\frac{1}{\sqrt{x}}

\newline

(C)

\frac{1}{2 \sqrt{x}} \cdot \frac{1}{x}

\newline

(D)

\frac{\sqrt{x} \ln (x)}{2}+\frac{1}{\sqrt{x}}

Differentiate $\sqrt{x}$ : Differentiate $\sqrt{x}$ with respect to $x$ to get $\frac{1}{2}x^{-\frac{1}{2}}$ . $\newline$ Differentiate $\ln(x)$ with respect to $x$ to get $\frac{1}{x}$ .
Differentiate $\ln(x)$ : Now apply the product rule: $h'(x) = (\sqrt{x})'(\ln(x)) + (\sqrt{x})(\ln(x))'$ . This gives us $h'(x) = (\frac{1}{2})x^{(-\frac{1}{2})}\ln(x) + (\sqrt{x})(\frac{1}{x})$ .
Apply product rule: Simplify the expression: $h'(x) = (\frac{1}{2})x^{(-\frac{1}{2})}\ln(x) + \frac{1}{2\sqrt{x}}$ . Oops, there's a mistake here. The second term should be $\frac{1}{2\sqrt{x}}$ without the $\ln(x)$ .