Basic Differentiation Rule

Q.

Find the derivative of $x^2+x\left(sinx\right)$ ?

1. 2x + x cos x + sin x

2. 2x + cos x + sin x

3. none of these

4. sin x + cosx

Q.

If $y=3x^2+2xthen\frac{dy}{dx}$=?

1. 8x

2. 

3. none of these

4. 6x + 2

Q.

If $y=x^2+5x^{\frac{3}{2}}+\frac{2}{x},then\frac{dy}{dx}=$ ?

1. 

2. 

3. 

4. none of these

Q. Match column A with their correct differentials in column B

$$\begin{array}{cccccc}& ColumnA& & ColumnB& & \\ p.& cosx& \left(i\right)& sinx& \left(v\right)& si{n}^{2}x\\ q.& tanx& \left(ii\right)& cosx& \left(vi\right)& se{c}^{2}x\\ r.& cosecx& \left(ii\right)& sinxcosx& \left(vii\right)& -cotxcosecx\\ s.& sinx& \left(iii\right)& tanxsecx& \left(viii\right)& cotxcosecx\\ t.& cotx& \left(iv\right)& -sinx& \left(ix\right)& -cose{c}^{2}x\end{array}$$​

1. p - (ii); q - (vi); r - (vii); s - (ii); t - (vii)

2. p - (ix); q - (v); r - (ix); s - (iv); t - (vi)

3. p - (iv); q - (vi); r - (vii); s - (ii); t - (ix)

4. p - (i); q - (iii); r - (vi); s - (i); t - (viii)

Q.

$y=\frac{sinx}{x+cosx},then\frac{dy}{dx}=?$

1. none of these

2. 

3. 

4. 

Q.

If y=x lnx, then $\frac{dy}{dx}$=?

1. 1 + lnx

2. 1

3. lnx

4. none of these

Q.

Can I differentiate any other function to get $3x^2$?

1. yes

2. No

Q.

Find the derivative of the following function with respect to x. $y=\frac{sinx}{x}$

1. 

2. 

3. 

4. 

Q.

If y=lnx, find $\frac{dy}{dx}$

1. 

2. 

3. 

4. 

Q.

Water pours out at the rate of Q from a tap, into a cylindrical vessel of radius r. find the rate at which the height of water level rises when the height is h.

1. 

2. 

3. 

4. none of these