y=(ax)^(n)+((b)/(x))^(m)

Differentiate (ax)^(m)+((b)/(x))^(n) with respect to 'x'.

Differentiate (ax)^(m)+((b)/(x))^(n) with respect to 'x'.

(ax)^(m)+(b)^(n)

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

If x^(n)=a^(m)cos^(4)theta and y^(n)=b^(m)sin^(4)theta then (i)(x^((n)/(2)))/((m)/(2))+(y^((n)/(2)))/(b^((m)/(2)))=1(ii)(x^(n))/(a^(m))+(y^(n))/(b^(m))=1( iii) (x^((n)/(2)))/(y^((n)/(2)))+(a^((m)/(2)))/(y^((m)/(2)))=1 (iv) None of these

Integral of the form: (ax+b)^(n)P(x)dx;P(x)/((ax+b)^(n))dx

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)