Advertisements
Advertisements
Question
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
Advertisements
Solution
`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
RELATED QUESTIONS
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. : `logx/(x^3-5)`
Find the derivative of the following function by the first principle: 3x2 + 4
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `2^x/logx`
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/-.
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx`if y = x log x (x2 + 1)
The supply S of electric bulbs at price P is given by S = 2P3 + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.
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 = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
