Let h(x)=log(x). Note: Here, we are referring to log base 10. Find h^('')(x). Choose 1 answer: (A) -(log(x))/(ln(10)) (B) -(1)/(x^(2)ln(10)) (C) -(1)/(x^(2)) (D) log(x)

Identify derivative of h(x): Identify the first derivative of h(x) = log(x). The first derivative of the logarithm function with respect to x is given by the formula: h'(x) = d/dx [log(x)] = 1/(xln(10))Differentiate h'(x): Differentiate h'(x) to find the second derivative h''(x). To find h''(x), we take the derivative of h'(x) with respect to x: h''(x) = d/dx [1/(xln(10))] Using the quotient rule or recognizing this as the derivative of a reciprocal function, we get: h''(x) = -1/(x^2ln(10))

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Let
h(x)=log(x).
Note: Here, we are referring to log base 10.
Find
h^('')(x).
Choose 1 answer:
(A)
-(log(x))/(ln(10))
(B)
-(1)/(x^(2)ln(10))
(C)
-(1)/(x^(2))
(D)
log(x)

Let $h(x)=\log (x)$ . $\newline$ Note: Here, we are referring to log base $10$ . $\newline$ Find $h^{\prime \prime}(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{\log (x)}{\ln (10)}$ $\newline$ (B) $-\frac{1}{x^{2} \ln (10)}$ $\newline$ (C) $-\frac{1}{x^{2}}$ $\newline$ (D) $\log (x)$

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Math Problems

Algebra 2

Properties of logarithms: mixed review

Full solution

Q. Let

h(x)=\log (x)

\newline

Note: Here, we are referring to log base

10

\newline

Find

h^{\prime \prime}(x)

\newline

Choose

1

answer:

\newline

(A)

-\frac{\log (x)}{\ln (10)}

\newline

(B)

-\frac{1}{x^{2} \ln (10)}

\newline

(C)

-\frac{1}{x^{2}}

\newline

(D)

\log (x)

Identify derivative of $h(x)$ : Identify the first derivative of $h(x) = \log(x)$ . The first derivative of the logarithm function with respect to $x$ is given by the formula: $h'(x) = \frac{d}{dx} [\log(x)] = \frac{1}{x\ln(10)}$
Differentiate $h'(x)$ : Differentiate $h'(x)$ to find the second derivative $h''(x)$ . To find $h''(x)$ , we take the derivative of $h'(x)$ with respect to $x$ : $h''(x) = \frac{d}{dx} \left[\frac{1}{x\ln(10)}\right]$ Using the quotient rule or recognizing this as the derivative of a reciprocal function, we get: $h''(x) = -\frac{1}{x^2\ln(10)}$