The differential coefficient of $f (Sin \,x)$ w.r.t. $x$ where $f (x) = \log\, x$ is
- Tan x
- Cot x
- f (Cos x)
- $\frac {1} {x}$
The Correct Option is B
Solution and Explanation
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
- 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 $f$ 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
- 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
Questions Asked in KCET exam
- If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are
- KCET - 2023
- limits of trigonometric functions
- The Curie temperatures of Cobalt and iron are 1400K and 1000K respectively. At T = 1600K , the ratio of magnetic susceptibility of Cobalt to that of iron is
- KCET - 2023
- Magnetism and matter
- A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the stataments is incorrect ?
- KCET - 2023
- Uniform Circular Motion
- The modulus of the complex number \(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\) is
- KCET - 2023
- complex numbers
- The energy gap of an LED is 2.4 eV. When the LED is switched ‘ON’, the momentum of the emitted photons is
- KCET - 2023
- Semiconductor electronics: materials, devices and simple circuits
Concepts Used:
Logarithmic Differentiation
Logarithmic differentiation is a method to find the derivatives of some complicated functions, using logarithms. There are cases in which differentiating the logarithm of a given function is simpler as compared to differentiating the function itself. By the proper usage of properties of logarithms and chain rule finding, the derivatives become easy. This concept is applicable to nearly all the non-zero functions which are differentiable in nature.
Therefore, in calculus, the differentiation of some complex functions is done by taking logarithms and then the logarithmic derivative is utilized to solve such a function.
SUBSCRIBE TO OUR NEWS LETTER
