Differentiate the following functions with respect to x: 10^ (10^… - Vidyadip

Question

Differentiate the following functions with respect to x:
$10^{(10^\text{x})}$

✓

Answer

Let $\text{y}=10^{(10^\text{x})}\ .....(\text{i})$
Taking log on both sides,
$\log\text{y}=\log_\text{e}10^{(10^\text{x})}$
$\log\text{y}=10^{\text{x}}\log_\text{e}10$
Differentiating with respect to x,
$\Rightarrow\ \frac{1}{\text{y}}\frac{\text{dy}}{\text{dx}}=\log_\text{e}10\times10^\text{x}\log_\text{e}10$
$\Rightarrow\frac{1}{\text{y}}\frac{\text{dy}}{\text{dx}}=10^\text{x}\times(\log_\text{e}10)^2$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{y}\big[10^{\text{x}}\times(\log_\text{e}10)^2\big]$
$\therefore\ \frac{\text{dy}}{\text{dx}}=10^{(10\text{x})}\times10^\text{x}\times(\log_\text{e}10)^2$
[Using equation (i)]

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that $\text{f}(\text{x})=\cos^2\text{x}$ is a decreasing function on $\Big(0,\frac{\pi}{2}\Big).$

Find the principal value of the following:
$\sec^{-1}\Big(2\sin\frac{3\pi}{4}\Big)$

Write the anti-derivative of $\Big(3\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}}\Big)$

Find fog and gof if:

$\text{f}(\text{x})=\text{c},\text{c}\in \text{R},\text{g(x)}=\sin \text{x}^2$

Find $x$, if $\left[\begin{array}{lll}x & -5 & -1\end{array}\right]\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]\left[\begin{array}{l}x \\ 4 \\ 1\end{array}\right]=0$

Evaluate the following integrals:
$\int\frac{\sec^2\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Evaluate the following integrals:
$\int5^{\text{x}+\tan^{-1}\text{x}}.\Big(\frac{\text{x}^2+2}{\text{x}^2+1}\Big)\text{dx}$

Find the angle between the following pairs of lines:

$\vec{\text{r}}=2\hat{\text{i}}-5\hat{\text{j}}+\hat{\text{k}}+\lambda\Big(3\hat{\text{i}}+2\hat{\text{j}}+6\hat{\text{k}}\Big)\ \text{and}$

$\vec{\text{r}}=7\hat{\text{i}}-6\hat{\text{k}}+\mu\Big(\hat{\text{i}}+2\hat{\text{j}}+2\hat{\text{k}}\Big)$

Find the values of a and b such that the function defined by
$\text{f(x)}=\begin{cases}5,&\text{if}\ \text{x}\leq{2}\\\text{ax} + \text{b},& \text{if}\ 2<\text{x}<10\\21,&\text{if}\ \text{x}\geq10\end{cases}$
is a continuous function.