Application of Derivative #!#Finding slope of a curve at any point

Application OF derivatives

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of the coordinates of the point.

The slope of work-time curve at any instant gives

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x,y)is(y-1)/(x^(2)+x)

Find the equation of the curve passing through origin if the slope of the tangent to the cuurve at any point (x,y) is equal to the square of the difference of the abscissa and ordinate of the point.

The equation of the curve, slope of whose tangent at any point (h, k) is 2k/h and which passes through the point (1, 1) is

Let us consider a curve, y=f(x) passing through the point (-2,2) and the slope of the tangent to the curve at any point (x,f(x)) is given by f(x)+xf'(x)=x^(2) . Then :

A curve passes through the point (3,-4) and the slope of.the is the tangent to the curve at any point (x,y) is (-(x)/(y)) .find the equation of the curve.

Find the equation of the curve passing through the point (-2,3) given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2))