Question

find the derivative of the following function
(a)LOGe3x
(b)log(2x+5)
(c)LOG10*x
(d)y=e*x*2

Answer 1

Dear student
$$\begin{gathered} \mathrm{Assuming}\mathrm{the}\mathrm{question}\mathrm{as}: \\ \mathrm{d})\mathrm{y}={\mathrm{e}}^{{\mathrm{x}}^2} \\ \mathrm{Differentiate}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{x}\mathrm{we}\mathrm{get} \\ \mathrm{y}\text{'}={\mathrm{e}}^{{\mathrm{x}}^2}\times \frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{x}}^2\right) \\ ={\mathrm{e}}^{{\mathrm{x}}^2}\times 2\mathrm{x} \\ =2\mathrm{x}{\mathrm{e}}^{{\mathrm{x}}^2} \\ \mathrm{b})\log (2\mathrm{x}+5) \\ \mathrm{Differentiate}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{x}\mathrm{we}\mathrm{get} \\ =\frac{1}{2\mathrm{x}+5}\times \frac{\mathrm{d}}{\mathrm{dx}}\left(2\mathrm{x}+5\right) \\ =\frac{1}{2\mathrm{x}+5}\times 2 \\ =\frac{2}{2\mathrm{x}+5} \end{gathered}$$
Similarly try others as a part of practise.
Regards