Advertisements
Advertisements
Question
Find `dy/dx if y = ((logx+1))/x`
Advertisements
Solution
`y=((logx + 1))/x`
Differentiating w.r.t. x, we get
`dy/dx=d/dx[(logx + 1)/x]`
= `(xd/dx(logx + 1) - (logx + 1)d/dx(x))/x^2`
= `(x(1/x + 0) - (logx + 1)(1))/x^2`
= `(1 - logx - 1)/x^2`
=`(-logx)/x^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
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. : `((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.
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 = x2 + 2x – 1
Find `dy/dx if y = "e"^x/logx`
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 = `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))`
