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: Nov 29, 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
1
Top Questions on Logarithmic Differentiation
- If $f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)$ and $g(x)=f(1) x^2+x f^{\prime}(x)+f^{\prime \prime}(x)$, then the value of $f(4)-g(4)$ is equal to ______
- JEE Main - 2023
- Mathematics
- Logarithmic Differentiation
Let $f$ be $a$ differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)>0;$ and $f(x)+\int\limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ Then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to _______
- JEE Main - 2023
- Mathematics
- Logarithmic Differentiation
- If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$, is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha$, $\beta$ are integers, then $\alpha+\beta$ is equal to :
- JEE Main - 2023
- Mathematics
- Logarithmic Differentiation
- Let $f: R \rightarrow R$ be a differentiable function such that $f^{\prime}(x)+f(x)=\int\limits_0^2 f(t) d t$If $f(0)=e^{-2}$, then $2 f(0)-f(2)$ is equal to_____
- JEE Main - 2023
- Mathematics
- Logarithmic Differentiation
- The value of \(\frac{1}{log_2N}+\frac{1}{log_3N}+\frac{1}{log_4N}+....\frac{1}{log_15N}\) is
- CUET (PG) - 2023
- Mathematics
- Logarithmic Differentiation
View More Questions
Questions Asked in KEAM exam
- A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 1011 N/m2,then change in the volume is:
- KEAM - 2023
- mechanical properties of solids
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- System of Particles & Rotational Motion
- The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
- KEAM - 2023
- Trigonometric Functions
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Integration by Parts
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- System of Particles & Rotational Motion
View More Questions