3.6 MCQ

If x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3) ?

• -25/27

• -7/27

• 7/27

• 3/4

• 25/27

If y=2cos(x/2), then d^2y/dx^2 =

• -8cos(x/2)

• -2cos(x/2)

• -sin(x/2)

• -cos(x/2)

• -1/2cos(x/2)

If dy/dx = x^4 -2x^3 + 3x -1, then d^3y/dx^3 evaluated at x = 2 is

• 11

• 24

• 26

• 125

If y=cosx - ln(2x), then d^3y/dx^3 =

• sin x -2/x^3

• -sin x -2/x^3

• sinx - 1/x^3

• -sinx - 1/x^3

If y=e^nx, then d^n y/dx^n =

• n^n e^nx

• n!e^nx

• ne^nx

• n^n e^x

• n! e^x

If y=sinx and y^{n} means the nth derivative of y with respect to x then the smallest positive integer for n for which y^(n) = y is

• 2

• 4

• 5

• 6

• 8

If f(x) = (2x+1)^4, then the 4th derivative of f(x) at x = 0 is

• 0

• 24

• 48

• 240

• 384

if f(x) = e^7x , then f^(7) (x) =

• 7*6*5*4*3*2

• 1/7^7 e^7x

• e^7x

• 7^7 e^7x

if y = e^2sin x , then d^2y/dx^2 =

• (4cos^2 x)(e^4sin x)

• (-4sinx cosx)(e^2sinx)

• (-sinx+cosx)(2e^2 sinx)

• (-sinx+2cos^2x)(2e^2 sinx)

if y = e^x^3 , then d^2y/dx^2 =

• 18x^3 e^x^3

• 9x^4 e^2x^3

• (6x+3x^2)e^x^3

• (6x+9x^4)e^x^3