The chain rule: if f(y) is a function of y and y is a function of x, then . Anytime you differentiate an expression in y, with respect to x, differentiate with respect to y and multiply by y'.

By the chain rule, the deirivative of , with respect to x, is . The derivative of , with respect to x, is . Of course, the derivative of , with respect to x, is . The derivative of the constant, 1, is, of course, 0. Put those together and solve for y'.

2.√x+√y=100

The derivative of , with respect to x, is and the derivative of , with respect to x, is [tex]\frac{1}{2}y^{-1/2}y'[tex]

Solve for y'.

The derivative of xy, with respect to x, is y+ xy'. The derivative of tan(y), with respect to x, is .3. xy=tan y

Solve for y'.

Thanks for those who will answer and I would be glad if you can explain to me how you got the answer..