Advertisements
Advertisements
प्रश्न
Differentiate the following function w.r.t.x. : `2^x/logx`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following function by the first principle: `x sqrtx`
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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 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 total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
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 = (sqrtx + 1/sqrtx)^2`
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/-.
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))`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
