Advertisements
Advertisements
Question
Differentiate the following function w.r.t.x. : `2^x/logx`
Solution
Let y = `2^x/logx`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" (2^x/logx)`
=` (log x d/dx (2^x) - 2^x d/dx (logx))/(logx)^2`
= `(log x. 2^x . log 2 - 2^x . 1/x)/(log x)^2`
= `[2^x (log x log 2 - 1/x)]/(log x)^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Differentiate the following function w.r.t.x. : `x/(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: 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: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
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`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = "e"^x/logx`
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
