Advertisements
Advertisements
Question
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
Advertisements
Solution
Let y =`1/sqrtx`
∴ `y =x^((-1)/2)`
Differentiating w.r.t. x, we get
`dy/dx=(-1)/2x^((-3)/2)`
= `(-1)/(2x^(3/2))`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
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.
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: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
Differentiate the following function w.r.t.x. : x−2
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = "e"^x/logx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
Differentiate the following w.r.t.x :
y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
