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List of top Mathematics 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 ______
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_____

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 _______

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 :
The value of \(\frac{1}{log_2N}+\frac{1}{log_3N}+\frac{1}{log_4N}+....\frac{1}{log_15N}\) is
If y=lognx, where logn means loge loge loge .....(repeated n times), then xlogx log2x log3x....log n-1 xlognx \(\frac{dy}{dx}\) is equal to :
Let f(x) = \(\displaystyle\sum_{k=1}^{10} kx^k\) , x ∈ R. If 2f(2) + f(2) = 190(2)n + 1 then n is equal to____. 
Find the general solution of the differential equation: \(\frac{dx}{x}+\frac{dy}{y}=0\)
If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)
If \(y(x) = (x^x)^x, \quad x > 0\), then \(\frac{d^2x}{dy^2} + 20\) at \(x = 1\) is equal to __________.
The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$ is _____.
Let \(f(x) =   \begin{cases}     \tan x,       & if\ 0\leq x\leq \frac{\pi}{4} \\      ax+b,       & if\ \frac{\pi}{4}\lt x\lt \frac{\pi}{2}   \end{cases}\), If f(x) is differentiable at \(x=\frac{\pi}{4}\), then the values of a and b are respectively
The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$ is _____.
Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is
If \(y= log(sec\ e^{x^2})\), then \(\frac {dy}{dx}\) =?
The general value of the real angle $\theta$, which satisfies the equation, (cos$\theta$ + i sin$\theta$) (cos2$\theta$ + i sin2$\theta$)........ (cosn$\theta$ + i sinn$\theta$) = 1 is given by, (assuming k is an integer)
Let $y = e^{2x}$ . Then $\left(\frac{d^{2}y}{dx^{2}}\right) \left(\frac{d^{2}x}{dy^{2}}\right) $ is
If \(\cos^{-1}(\frac{y}{b})=\log(\frac{x}{n})^x\), then x2y2 + xy1 =
The differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ is
The derivative of $y = x^{\sin\,x}$ is
If $\log _{0.2}(x-1)>\log _{0.04}(x+5)$, then
If $ f(x) = log_x $ { $ ln(x) $ },then $ f'(e) $ is equal to
If $\log_{7} \,2 = ?$, then the value of $\log_{49}\, \left(28\right)$ is
$\frac{d}{dx} (x^x)$ is equal to
The differential coefficient of $f (Sin \,x)$ w.r.t. $x$ where $f (x) = \log\, x$ is

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