Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Advertisements
उत्तर
Let y =`logx/(x^3-5)`
Differentiating w.r.t. x, we get
`dy/dx= d/dx(logx/(x^3 - 5))`
= `((x^3 - 5)d/dx(logx) - (logx)d/dx(x^3 - 5))/((x^3 - 5)^2)`
=`((x^3 - 5)(1/x) - logx(d/dx(x^3) - d/dx(5)))/((x^3 - 5)^2)`
= `((x^3 - 5)1/x - logx(3x^2 - 0))/((x^3 - 5)^2)`
= `((x^3 - 5)1/x - log x * 3x^2)/(x^3 - 5)^2`
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
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 : `(x^2 + 1)/x`
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: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Find `dy/dx if y = ((logx+1))/x`
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.
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 = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
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))`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
