Find the rate of change of q with respect to p when?

Question

p= 20 / (q^2+5)

A) -10 / qp
B) -10/ qp^2
C) -5 / qp^2
D) -5 / q^2p

Answer 1

p = 20 / (q^2+5)
q^2 + 5 = 20/p
2qdq = -20dp/p^2
dq/dp = -10/qp^2

Answer 2

p = 20/(q^2+5)

= 20 * (q^2+5)^-1

use a substitution for a differential chain rule.

If z=(q^2+5)

p = 20 * z^-1

dp/dq = dp/dz * dz/dq

= 20 (-1)z^-2 * 2q

= 20 {-(q^2+5)^-2} * 2q = -40q(q^2+5)^-2

invert,

dq/dp = -(1/40q)(q^2+5)^2

but (q^2+5) = 20/p

so dq/dp can be expressed as

dq/dp = -(1/40q) (20/p)^2 = -(1/40q) (400 p^-2)
=-10/qp^2.

Answer 3

LET dP/dQ =Y'
SO
Y'
= -20*(2Q) / {(Q^2+5)^2}

BUT 20 / (q^2+5) = P & (q^2+5) = 20 /P

= -2PQ / (Q^2+5)

= -P^2 *Q /10

SO

rate of change of q with respect to P =1 / Y'
=-10/[Q*P^2]...............ANS..................[""B"""]