Rules of Differentiation (Without Proof)

Differentiate the following w.r.t.x :

y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`

Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`

The demand function of a commodity is given as P = 20 + D − D². Find the rate at which price is changing when demand is 3.

If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.

The supply S for a commodity at price P is given by S = P² + 9P − 2. Find the marginal supply when price is 7/-.

Differentiate the following function .w.r.t.x. : x⁵

Find `dy/dx if y=(sqrtx+1)^2`

Find `dy/dx if y=(1+x)/(2+x)`