If y = _ 10 x^2 , then dy dx is equal to - Vidyadip

MCQ

If $y = {\log _{10}}{x^2}$, then ${{dy} \over {dx}}$ is equal to

A
${2 \over x}$
✓
${2 \over {x{{\log }_e}10}}$
C
${1 \over {x{{\log }_e}10}}$
D
${1 \over {10x}}$

✓

Answer

Correct option: B.

${2 \over {x{{\log }_e}10}}$

b
(b) Given $y = {\log _{10}}{x^2}$

$y = \frac{{{{\log }_e}{x^2}}}{{{{\log }_e}10}}$, $\left( \because {{\log }_{a}}b=\frac{{{\log }_{e}}b}{{{\log }_{e}}a} \right)$

$y = \frac{{2{{\log }_e}x}}{{{{\log }_e}10}}$,

$\therefore \frac{{dy}}{{dx}} = \frac{2}{{x{{\log }_e}10}}$.

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 "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The maximum number of equivalence relations on the set $A = \{1, 2, 3\}$ is:

${\sin ^{ - 1}}\frac{1}{{\sqrt 5 }} + {\cot ^{ - 1}}3 $ is equal to

A function $f: R \rightarrow R$ defined as $f(x)=x^2-4 x+5$ is:

The general solution of the differential equation $\text{e}^\text{x}\ \text{dy}+(\text{y e}^\text{x}+2\text{x})\text{dx}=0\ \text{is}$

Out of $30$ consecutive integers$, 2$ are chosen at random. The probability that their sum is odd, is

$\int_{\,0}^{\,\infty } {\frac{{x\ln x\,dx}}{{{{(1 + {x^2})}^2}}}} $ is equal to

If $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = $ $\left| {\,\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lambda - 1}&{\lambda + 3}\\{\lambda + 1}&{2 - \lambda }&{\lambda - 4}\\{\lambda - 3}&{\lambda + 4}&{3\lambda }\end{array}\,} \right|,$ the value of $t$ is

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12\,A$ is equal to $...........$.

If $A$ and $B$ are such that $\text{P}(\text{A}\cup\text{B})=\frac{5}{9}$ and $\text{P}(\overline{\text{A}}\cup\overline{\text{B}})=\frac{2}{3},$ then $\text{P}(\overline{\text{A}})+\text{P}(\overline{\text{B}})=$

The set of all values of $\lambda $ for which the system of linear equations $x - 2y - 2z = \lambda x$ ; $x + 2y + z = \lambda y$ ; $-x - y = \lambda z$ has non zero solutions.