Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Advertisements
उत्तर
Let y = `sqrt(x) + tan x - x^3`
∴ `("d"y)/("d"x) = "d"/("d"x) (sqrt(x) + tan x - x^3)`
= `"d"/("d"x)(sqrt(x)) + "d"/("d"x) (tanx) - "d"/("d"x)(x^3)`
= `1/(2sqrt(x)) + sec^2x - 3x^2`.
APPEARS IN
संबंधित प्रश्न
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: `x sqrtx`
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
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 demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
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. : `xsqrt x`
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
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`
Find `dy/dx`if y = x log x (x2 + 1)
The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.
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 = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
