Advertisements
Advertisements
Question
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Advertisements
Solution
Let y = `(x^2 + 1)/x`
Differentiating w.r.t. x, we get
`dy/dx= d/dx((x^2 + 1)/x)`
= `(xd/dx(x^2 + 1) - (x^2 + 1)d/dx(x))/x^2`
= `(x(2x + 0) - (x^2 + 1)(1))/x^2`
= `(2x^2 - x^2 - 1)/x^2`
`dy/dx=(x^2 - 1)/x^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following function by the first principle: 3x2 + 4
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. : `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: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
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/-.
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))`
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)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
