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. : `(xe^x)/(x+e^x)`
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
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.
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.
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 = x2 + 2x – 1
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx`if y = x log x (x2 + 1)
The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.
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.
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^(4/3) + "e"^x - sinx`
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))`
