Advertisements
Advertisements
Question
Find `dy/dx`if y = x log x (x2 + 1)
Solution
y = x log x (x2 + 1)
Differentiating w.r.t. x, we get
`dy/dx = d/dx(x)(logx)(x^2 + 1)`
= `(x)(logx)d/dx(x^2 + 1) - (x^2 + 1)d/dx((x)(logx))`
= `(xlogx)(2x + 0) + (x^2 + 1)[xd/dx(logx) + (logx)d/dx(x)]`
=`2x^2logx + (x^2 + 1)[x xx 1/x + (logx)(1)]`
= 2x2 log x + (x2 + 1) (1 + log x)
= 2x2 log x + (x2 + 1) + (x2 + 1) log x
APPEARS IN
RELATED QUESTIONS
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
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.
Differentiate the following function .w.r.t.x. : x5
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 = "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 demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
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 = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
