Exponential and Logarithmic Functions

If $y={\left(\frac{x}{n}\right)}^{nx}\left(1+\log \frac{x}{n}\right)$ then $y\text{'}\left(n\right)$ is given by

If $y=\log x+{\log }_{5}x+{\log }_{5}5$, then $\frac{dy}{dx}$ is

Find $\frac{d}{dx}\left(e^{5x+3}\right)$.

If $y=2^{\sin x}$, then $\frac{dy}{dx}$ is equal to

If $y=4^x$, then $\frac{dy}{dx}$ is

If $y=\left(1+x\right)\left(1+x^2\right)\left(1+x^4\right)\dots \left(1+x^{2^n}\right)$, then $\frac{dy}{dx}$ at $x=0$ is:

If $\mathrm{y}=2^{\mathrm{x}}\mathrm{ }{3}^{2\mathrm{x}}\mathrm{ }{5}^{-\mathrm{x}}\mathrm{ }{7}^{-\mathrm{x}}$ then $\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}=$

${10}^{-x\tan x}\left[\frac{d}{dx}\left({10}^{x\tan x}\right)\right]$ is equal to

If $\log \left(x+y\right)-2xy=0$. Then $y^{\text{'}}\left(0\right)=$

The angle at which curve $y=k{e}^{kx}$, intersects the $y$-axis is

Which function of management involves monitoring the work of employees to ensure they are meeting performance standards?

Which measure of GDP adjusts for price changes over time?

Which of the following best describes the GDP Deflator?

Which formula is used to calculate Real GDP?

What is the primary function of controlling in a business context?

Which of the following is NOT a function of controlling in a business?

${\left\{\frac{d\left(x^x+x^{x+1}+x^{x+2}\right)}{dx}\right\}}_{x=e}=\_\_\_\_\_\_\_\_$

If $y=x{e}^{xy}$ and $\frac{dy}{dx}=\frac{{\displaystyle y\left(1+u\right)}}{x\left(1-u\right)},$ then $u=$