Derivative Quiz

Which of the following is / are true ?

• $\left(50x^2\right)^I\ =\ 100$

• $\left(\sqrt{2}-\Pi\right)^I\ =\ 0$

• $\left(-2x\right)^I\ =\ -2$

Which of the following is / are true ?

• $\left(-x^2\right)^I\ =\ -2x^2$

• $\left(2x^3\right)^I\ =\ 6x^2$

• $\left(\ 4x\ -2x^3\right)^I\ =\ 4\ -\ 6.x^2$

Which of the following is / are true ?

• $\left(-\sin x\right)^I\ =\ -\cos x$

• $\left(\cos x\right)^I\ =\ -\sin x$

• $\left(\cos x-\sin x\right)^I\ =\ -\cos x-\sin x$

Which of the following is / are true ?

• $\left(\ u\ +v\right)^I\ =\ u^I\ +\ v^I$

• $\left(u\ -\ v\right)^I\ =\ u^I\ -\ v^I$

• $\left(\ u.v\right)^I\ =\ u^I.v\ -\ v^I.u$

• $\left(\frac{u}{v}\right)^I\ =\ \frac{u^I.v\ +\ v^I.u}{v^2}$

Derive y = 2x³ - 3x²+2

• 6x - 6

• 6x² - 6x

• 6x² - 6

• 6x³ - 6x²

Find the derivative of the given equation

f(x) = x⁴ - 4x³ - 4x

• 4x³ - 4x² - 4

• 4x³ - 12x² - 4

• 4x² - 12x - 4

• 4x³ - 12x² - 4x

Find the derivative of
f(x) =  $-\frac{1}{x}$  

•  $\frac{1}{2x}$  

•  $-x^{-1}$  

•  $\frac{1}{x^2}$  

• -x^-2

Find the second derivative of :

f (x) = x² - x⁵

• f ''(x)= 2 - 20x

• f ''(x) = 2 - 20x⁴

• f ''(x) = 2x - 20x³

• f ''(x) = 2 - 20x

Derive y = cos 2x with respect to x.

• 2.sin 2x
  

• -2.sin 2x

• -sin 2x
  

• sin 2x
  

Find the derivative of
 $g\left(x\right)=\frac{2x}{x+1}$  

•  $\frac{2}{\left(x+1\right)^2}$  
  

•  $\frac{-2}{\left(x+1\right)^2}$  

•  $\frac{2x}{\left(x+1\right)^2}$  
  

•  $\frac{-2x}{\left(x+1\right)^2}$