Derive the equation of tangent and normal at `(x_(0),y_(0))` of the curve y= log x

Find the equations of tangent and normals to the curves y=(1)/(1+x^(2)) at (0,1)

Find the equations of tangent and normals to the curves y=sin x+cos x at x=(pi)/(3)

(i) Find the equation of tangent to curve y=3x^(2) +4x +5 at (0,5) (ii) Find the equation of tangent and normal to the curve x^(2) +3xy+y^(2) =5 at point (1,1) on it (iii) Find the equation of tangent and normal to the curve x=(2at^(2))/(1+t^(2)) ,y=(2at^(2))/(1+t^(2)) at the point for which t =(1)/(2) (iv) Find the equation of tangent to the curve ={underset(0" "x=0)(x^(2) sin 1//x)" "underset(x=0)(xne0)" at "(0,0)

Find the equations of the tangent and the normal to the curve y^2=4a x at (x_1,\ y_1) at indicated points.

Find the equation of the tangent and the normal to the curve y = x^(2) + 4x + 1 at the point where x = 3

Find the equations of the tangent and the normal to the curve y=x^2+4x+1 at x=3 at the indicated points

Find the equations of the tangent and the normal to the curve x+y=5, where the tangent is parallel to the line 2x-y+1=0

Find the equations of the tangent and the normal to the curve y=x^2 at (0,\ 0) at the indicated points

Find the equations of the tangent and the normal to the curve y (x -2) (x -3) - x + 7 = 0 at the point where it cuts the x-axis

Find the equations of the tangent and the normal to the curve 16x^(2)+9y^(2)=145 at the point (x_(1),y_(1)), where x_(1)=2 and y_(1)>0