Question:
If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)
If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)
Updated On: Dec 21, 2024
- \(6e^{3\log(2x+1)}\)
- \(6\frac{e^{3\log(2x+1)}}{2x+1}\)
- \(\frac{e^{3\log(2x+1)}}{2x+1}\)
- \(\frac{e^{3\log(2x+1)}}{3(2x+1)}\)
- \((2x+1)e^{3\log(2x+1)}\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B) : \(6\frac{e^{3\log(2x+1)}}{2x+1}\)
Was this answer helpful?
0
2
Top Questions on Logarithmic Differentiation
- Evaluate the integral: \[ \int \frac{6x^3 + 9x^2}{x^4 + 3x^3 - 9x^2} dx. \]
- KEAM - 2024
- Mathematics
- Logarithmic Differentiation
- If \[ y = \log_e \left( \frac{1 + 2x^2}{1 - 3x^2} \right), \] then \( \frac{dy}{dx} \) is:
- KEAM - 2024
- Mathematics
- Logarithmic Differentiation
- If \[ x^4 + 2\sqrt{y} + 1 = 3, \] then \( \frac{dy}{dx} \) at \( (1,0) \) is equal to
- KEAM - 2024
- Mathematics
- Logarithmic Differentiation
- Given that \( y = (\sin x)^x \cdot x^{\sin x} + a^x \), find \( \frac{dy}{dx} \).
- CBSE CLASS XII - 2024
- Mathematics
- Logarithmic Differentiation
- If \( x^y = e^x - y \), prove that \( \frac{dy}{dx} = \frac{\log x (1 + \log x)^2}{1 + \log x} \).
- CBSE CLASS XII - 2024
- Mathematics
- Logarithmic Differentiation
View More Questions
Questions Asked in KEAM exam
- In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
- KEAM - 2024
- Dimensional Analysis
- If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
- KEAM - 2024
- Integration
- An organic compound contains 37.5% C, 12.5% H and the rest oxygen. What is the empirical formula of the compound?
- KEAM - 2024
- Oxygen
- Let A, B, C denote the set of students in a college who play football, basketball, and cricket respectively. If \( n(A) = 60 \), \( n(B) = 55 \), \( n(C) = 70 \), \( n(A \cup B \cup C) = 100 \) and \( n(A \cap B \cap C) = 20 \), then the number of students who play exactly two of these sports is
- KEAM - 2024
- Relations and functions
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
- KEAM - 2024
- Grignard’s reagents and their uses
View More Questions