Question

Derivative of $\frac{\ln \left(x^3\right)\times \left(x^3\right)}{{\left(2\right)}^x}$ at x = 1 is

• A. 1
• B. 1.5
• C. 3

Answer 1

The correct option is B 1.5

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{d\frac{\ln \left(x^3\right)\times \left(x^3\right)}{{\left(2\right)}^x}}{\mathrm{dx}}$

= $\frac{\left(3x^2+3x^2\ln \left(x^3\right)\right]{\left(2\right)}^x-\left(\ln \left(x^3\right)x^3\right]2^x\ln 2}{2^{2x}}=\frac{3x^2\left(1+3\mathrm{lnx}\right)2^x-3x^3\mathrm{lnx}{\left(2\right)}^x\ln 2}{2^{2x}}{\frac{\mathrm{dy}}{\mathrm{dx}}}_{x=1}=\frac{3\left(1+0\right)2^1-0}{4}=1.5$