Advertisements
Advertisements
Question
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Advertisements
Solution
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x) (7^x + x^7 - 2/3 xsqrt(x) - log x + 7^7)`
∴ `("d"y)/("d"x) = "d"/("d"x) (7^x) + "d"/("d"x) (x^7) - 2/3 "d"/("d"x) (x^(3/2)) - "d"/("d"x) (logx) + "d"/("d"x) 7^7`
= `7^x log 7 + 7x^6 - 2/3 xx 3/2 x^(3/2 - 1) - 1/x + 0`
= `7^x log 7 + 7x^6 - x^(1/2) - 1/x`
= `7^x log 7 + 7x^6 - sqrt(x) - 1/x`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
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: 3x2 + 4
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"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: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
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. : x5
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 = x^2 + 1/x^2`
Find `dy/dx` if y = x2 + 2x – 1
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 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.
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 = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
