Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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) h(x)=\log (x) .\newlineNote: Here, we are referring to log base 1010.\newlineFind h(x) h^{\prime \prime}(x) .\newlineChoose 11 answer:\newline(A) log(x)ln(10) -\frac{\log (x)}{\ln (10)} \newline(B) 1x2ln(10) -\frac{1}{x^{2} \ln (10)} \newline(C) 1x2 -\frac{1}{x^{2}} \newline(D) log(x) \log (x)

Full solution

Q. Let h(x)=log(x) h(x)=\log (x) .\newlineNote: Here, we are referring to log base 1010.\newlineFind h(x) h^{\prime \prime}(x) .\newlineChoose 11 answer:\newline(A) log(x)ln(10) -\frac{\log (x)}{\ln (10)} \newline(B) 1x2ln(10) -\frac{1}{x^{2} \ln (10)} \newline(C) 1x2 -\frac{1}{x^{2}} \newline(D) log(x) \log (x)
  1. Identify derivative of h(x)h(x): Identify the first derivative of h(x)=log(x)h(x) = \log(x). The first derivative of the logarithm function with respect to xx is given by the formula: h(x)=ddx[log(x)]=1xln(10)h'(x) = \frac{d}{dx} [\log(x)] = \frac{1}{x\ln(10)}
  2. Differentiate h(x)h'(x): Differentiate h(x)h'(x) to find the second derivative h(x)h''(x). To find h(x)h''(x), we take the derivative of h(x)h'(x) with respect to xx: h(x)=ddx[1xln(10)]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)=1x2ln(10)h''(x) = -\frac{1}{x^2\ln(10)}

More problems from Properties of logarithms: mixed review