Advertisements
Advertisements
प्रश्न
Find `dy/dx`if y = x log x (x2 + 1)
Advertisements
उत्तर
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
संबंधित प्रश्न
Differentiate the following function w.r.t.x. : `x/(x + 1)`
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+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: 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 total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
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
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
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 = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
