Find the value of dy/dx

Find the values of (dy)/(dx) , if y = x^(tanx)+sqrt((x^(2)+1)/(2)) .

If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), find the values of (dy)/(dx) at t=pi/4 and t=pi/3dot

If y = log_(10) x , then the value of (dy)/(dx) is

If the tangent line at a point (x ,\ y) on the curve y=f(x) is parallel to y-axis, find the value of (dx)/(dy) .

If y =(x-a)(x-b) then find the value of x when (dy)/(dx)=0 .

Find dy/dx using the rule dy/dx=(dy)/(du)⋅(du)/(dv)⋅(dv)/(dx) : y=cos^(-1)sqrt(2x-3)

Find the sum of the order and degree of the differential equation: (dy)/(dx)=x""(dx)/(dy) .

If y=x^sinx ,then find dy/dx=

In (dy)/(dx),\ x is independent variable and y is the dependent variable. If independent and dependent variables are interchanged (dy)/(dx) becomes (dx)/(dy) and these two are connected by the relation (dy)/(dx)dot(dx)/(dy)=1 . Find a relation between (d^2y)/(dx^2) and (d^2x)/(dy^2)

Find the order and degree of the following differential equation: (dy)/(dx)+y=1/((dy)/(dx))