Question

Derivative of the function, $f\left(x\right)=2\ln {\left(x\right)}^5+2\ln {\left(x\right)}^3+\ln {\left(x\right)}^2-\ln \left(x\right)+2x$ is

• A. $2$
• B. $\frac{17}{x}+2$
• C. $\frac{19}{x}+2$

Answer 1

The correct option is B $\frac{17}{x}+2$

$f\left(x\right)=2\ln {\left(x\right)}^5+2\ln {\left(x\right)}^3+\ln {\left(x\right)}^2-\ln \left(x\right)+2xf\text{'}\left(x\right)=\frac{d}{\mathrm{dx}}\left(10\ln \left(x\right)+6\ln \left(x\right)+2\ln \left(x\right)-\ln \left(x\right)+2x\right)\because \ln {\left(p\right)}^r=r\times \ln \left(p\right)=17\frac{d\left(\ln \left(x\right)\right)}{\mathrm{dx}}+2\frac{d\left(x\right)}{\mathrm{dx}}=\frac{17}{x}+2$