Derivative of One Function w.r.t Another

Q.

What is the differentiation of$\log 2x$?

Q.

If $y=\mathrm{loglog}x$, then $e^y\frac{dy}{dx}=$

1. $\frac{1}{x}$

2. $\frac{1}{x\log x}$

3. $\frac{1}{\log x}$

4. $e^y$

Q.

The derivative of $F\left[f\left\{\phi \left(x\right)\right\}\right]$ is

1. $F\left[f\left\{\phi \left(x\right)\right\}\right]$

2. $F\left[f\left\{\phi \left(x\right)\right\}\right]f\left\{\phi \left(x\right)\right\}$

3. $F\left[f\left\{\phi \left(x\right)\right\}\right]f\left\{\phi \left(x\right)\right\}\phi \left(x\right)$

4. none of these

Q.

${\log }_e\frac{(1+3x)}{(1-2x)}$ is equal to

1. $-5x–\frac{5x^2}{2}–\frac{35x^3}{3}–\dots$

2. $-5x+\frac{5x^2}{2}–\frac{35x^3}{3}+\dots$

3. $5x–\frac{5x^2}{2}+\frac{35x^3}{3}–\dots$

4. $5x+\frac{5x^2}{2}+\frac{35x^3}{3}+\dots$

Q.

Find the difference $\left(\frac{1}{2}h+7\right)-\left(\frac{3}{2}h+9\right)$

Q. $Ify=sinxandz=5,then\frac{dy}{dz}$ = _____

1. cos x
2. –cosx
3. 5
4. Does not exist

Q.

Derivative of $log|x|$ w.r.t. $|x|$ is

1. $\frac{1}{x}$

2. $\frac{1}{|x|}$

3. $\pm \frac{1}{x}$

4. None of these

Q. Let $f:R\to R$ be a one-one onto differentiable function, such that f(2) = 1 and f '(2) = 3. Then the value of ${\left(\frac{d}{\mathrm{dx}}\left(f^{-1}\left(x\right)\right)\right)}_{x=1}$ is

1. 1
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. 3

Q. The derivative of $si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ with respect to $ta{n}^{-1}\left(\frac{2x}{1-x^2}\right)$ is

1. $0$
2. $1$
3. $\frac{1}{1-x^2}$
4. $\frac{1}{1+x^2}$

Q.

Simplify $\frac{18}{25}÷\frac{6}{25}$

Q.

Simplify the expressions

$\frac{5}{3}\left(\frac{4}{3}a+9b+\frac{2}{3}a\right)$

Q. The derivative of $si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ with respect to $ta{n}^{-1}\left(\frac{2x}{1-x^2}\right)$ is

1. $0$
2. $1$
3. $\frac{1}{1-x^2}$
4. $\frac{1}{1+x^2}$

Q.

Find the value of $\frac{4j+h}{5},whereh=3andj=4$

Q.

Find $\frac{2}{3}\mathrm{of}2\frac{3}{8}$