Home
Class 12
MATHS
If y=(1)/(3).(a^(2)-b^(2))/(a^(2)+b^(2))...

If `y=(1)/(3).(a^(2)-b^(2))/(a^(2)+b^(2)).x[(p)/(p+1).psqrt(x)+(q)/(q+1).q sqrt(x)]`, prove that,
`(dy)/(dx)=((a+b)/(a-b))^((q+p)/(q-p))" at "x=((a+b)/(a-b))^((2pq)/(q-p))`

Promotional Banner

Similar Questions

Explore conceptually related problems

If log_(p)x=a and log_(q)x=b prove that log_(p/q)x=(ab)/(a-b)

Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

Simply (x^(p)/x^(q))^(p+q)div((x^(p+q))/(x^(p-q)))^(p^(2)/(q))

If x = [-(q)/(2) + sqrt((q^(2))/(4) + (p^(3))/(27))]^((1)/(3)) + [-(q)/(2) - sqrt((q^(2))/(4) + (p^(3))/(27))]^((1)/(3)) then prove that x^(3) + pq + q = 0

If f(x)=e^(px+q) [p and q are constants], show that, f(a).f(b).f(c)=f(a+b+c).e^(2q)

tan ^(-1)""(1)/(p+q)+tan ^(-1)""(q)/(p^(2)+pq+1)=cot^(-1)p

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

Prove root(p+q)(x^(p^(2))/(x^(q^(2))))xxroot(q+r)(x^(q^(2))/(x^(r^(2))))xxroot(r+p)(x^(r^(2))/(x^(p^(2))))=1

Factorise : p^(2)+2p-(q+1)(q-1)