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 w. r. t. x. : `(xe^x)/(x+e^x)`
Find the derivative of the following function by the first principle: 3x2 + 4
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `2^x/logx`
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: 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 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. : x−2
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx`if y = x log x (x2 + 1)
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
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 = `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)`
