Advertisements
Advertisements
प्रश्न
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
उत्तर
`y = x^3 – 2x^2 + sqrtx +1`
Differentiating w.r.t. x, we get
`dy/dx=d/dx(x^3-2x^2+sqrtx+1)`
=`d/dx(x^3)-2d/dx(x^2)+d/dx(sqrtx)+d/dx(1)`
= `3x^2-2(2x)+d/dx(x^(1/2))+0`
=`3x^2-4x+1/2x^(1/2-1)`
=`3x^2-4x+1/2x^((-1)/2)`
`dy/dx=3x^2-4x+1/(2sqrtx)`
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
Solve the following example: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Differentiate the following function w.r.t.x. : x−2
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
