Question

if y= ax2+bx+c where a,b,c are constant then y3(d2y/dx2) =?​

Answer 1

Answer:

it is also constant

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Answer 2

y

2

=ax

2

+bx+c

⇒2y

dx

dy

=

dx

d

(ax

2

)+

dx

d

(bx)+

dx

d

(c)

⇒2y

dx

dy

=2ax+b+0

⇒2

dx

d

(y

dx

dy

)=

dx

d

(2ax+b)

⇒2(

dx

dy

)

2

+2y

dx

2

d

2

y

=2a

⇒(

dx

dy

)

2

+y

dx

2

d

2

y

=a

⇒y

dx

2

d

2

y

=a−(

dx

dy

)

2

⇒y

dx

2

d

2

y

=a−(2ax+b)

2

⇒y

3

dx

2

d

2

y

=y

2

(a−(2ax+b)

2

)

=(ax

2

+bx+c)(a−4a

2

x

2

−b

2

−4axb) is a function of x only