Differentiate the following functions with respect to x: _7(2x-3) - Vidyadip

Question

Differentiate the following functions with respect to x:
$\log_7(2\text{x}-3)$

✓

Answer

Let, $\text{y}=\log_7(2\text{x}-3)$
$\Rightarrow\ \text{y}=\frac{\log(2\text{x}-3)}{\log_7}\ \Big[\text{Since}, \log^\text{b}_\text{a}=\frac{\log\text{b}}{\log\text{a}}\Big]$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\log7}\frac{\text{d}}{\text{dx}}\big(\log(2\text{x}-3)\big)$
$=\frac{1}{\log7}\times\frac{1}{(2\text{x}-3)}\frac{\text{d}}{\text{dx}}(2\text{x}-3)$
[Using chain rule]
$=\frac{2}{(2\text{x}-3)\log7}$
Hence, $\frac{\text{d}}{\text{dx}}(\log_7(2\text{x}-3))=\frac{2}{(2\text{x}-3)\log7}$

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 Question" from Differentiation→Differentiation — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evalute the following integrals:
$\int\frac{\sin2\text{x}}{\sin5\text{x}\sin3\text{x}}\text{dx}$

Solve the equation
$\cos^{-1}\frac{\text{a}}{\text{x}}-\cos^{-1}\frac{\text{b}}{\text{x}}=\cos^{-1}\frac{1}{\text{b}}-\cos^{-1}\frac{1}{\text{b}}-\cos^{-1}\frac{1}{\text{a}}$

If $\text{A}=\begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix},$ and $\text{A}^{-1}=\text{A}',$ find value of $\alpha.$

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? $($Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $\frac{1}{2} ).$

If the lines $\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{2\text{k}}=\frac{\text{z}-3}{2}\ \text{and}\ \frac{\text{x}-1}{3\text{k}}=\frac{\text{y}-1}{1}=\frac{\text{z}-6}{-5}$ are perpendicular, find the value of k.

Evaluate the definite integral $\int\limits_2^3 {\frac{{xdx}}{{{x^2} + 1}}} $

Evaluate the following integrals:
$\int\cot \text{x}. \text{log}\ \sin\text{x dx}$

If $\text{y}=\log\Big(\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}}\Big),$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}-1}{2\text{x}(\text{x}+1)}$

Sand is being poured onto a conical pile at the constant rate of $50\ cm^3/$ minute such that the height of the cone is always one half of the radius of its base. How fast is the height of the pile increasing when the sand is $5\ cm$ deep.

Write the following function in the simplest form:
$\tan^{-1}\bigg(\frac{3a^{2}x-x^{3}}{a^{3}-3ax^{2}}\bigg), a>0; \frac{-a}{\sqrt{3}}\leq x\leq\frac{a}{\sqrt{3}}$