Advertisements
Advertisements
Question
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Advertisements
Solution
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
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
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 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
Differentiate the following function w.r.t.x. : x−2
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx if y = "e"^x/logx`
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^(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))`
