## Differentiation Quiz

Important topics for Maths has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with the day-to-day experiences.

Q1. The first derivative of the function [cos^(-1)⁡(sin⁡√((1+x)/2))+x^x] with respect to x at x=1 is
•  3/4
•  0
•  1/2
•  -1/2
Solution

Q2.If y=ax^(n+1)+bx^(-n), then x^2 (d^2 y)/(dx^2 ) is equal to
•  n(n-1)y
•  n(n+1)y
•  ny
•  n^2y
Solution

Q3.  A function f satisfies the condition, f(x)=f'(x)+f"(x) + f'''(x)+⋯ where f(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1, then f(x) is
•   e^(x/2)
•  e^x
•  e^2x
•  e^4x
Solution
(a) Given f=f^'+f''"+" f'''+⋯∞ ⇒f^'=f''"+" f'''+f''''+⋯∞ ⇒f-f^'=f' ⇒f=2f' Hence, f'/f=1/2⇒∫f'/f dx=∫1/2 dx ⇒log⁡f(x)=x/2+c ⇒f(x)=e^(x/2+c) Also, f(0)=1⇒c=0⇒f(x)=e^(x/2)

Q4.

•  -5
•  1/5
•  5
•  None of these
Solution

Q5.

•  √Ï€/6
•  -√Ï€/6
•  1/√6
•  Ï€/√6
Solution
(b) f(x)=√(1+cos^2⁡(x)^2)

Q6. 36. If y^(1/m)=(x+√(1+x^2)), then (1+x^2 ) y_2+xy_1 is (where y_r represents rth derivative of y w.r.t. x)
•  m^2 y
•  my^2
• m^2 y^2
•  None of these
Solution

Q7.A function f, defined for all positive real numbers, satisfies the equation f(x^2 )=x^3 for every x>0. Then the value of f^' (4)=
•  12
•  3
•  3/2
•  Cannot be determined
Solution
(b) 2xf'(x^2 )=3x^2 ⇒ 4f'(2)=12⇒f'(4)=3

Q8. If y=x^(x^x), then dy/dx is
•  y[x^x(log⁡ex) log⁡x+x^x]
•  y[x^x(log⁡ex ) log⁡x+x]
•  y[x^x(log⁡ex) log⁡x+x^(x-1)]
•  y[x^x(log_e⁡x) log⁡x+x^(x-1) ]
Solution

Q9.d/dx cos^(-1)⁡√(cos⁡x ) is equal to
•  1/2 √(1+sec⁡x)
•  √(1+sec⁡x)
•  -1/2 √(1+sec⁡x)
•  -√(1+sec⁡x)
Solution

Q10. If y=asin⁡x + bcos⁡x, then y^2+ (dy/dx)^2is a
•  function of x
•  function of y
•  function of x and y
• constant
Solution

#### Written by: AUTHORNAME

AUTHORDESCRIPTION

## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: Differentiation-Quiz-4
Differentiation-Quiz-4