Advertisements
Advertisements
प्रश्न
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = sin(x – 2) + x2
उत्तर
y = sin(x – 2) + x2
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[sin(x - 2) + x^2]`
= `"d"/"dx"[sin(x - 2)] + "d"/"dx"(x^2)`
= `cos(x - 2)."d"/"dx"(x - 2) + 2x`
= cos(x – 2).(1 – 0) + 2x
= cos(x – 2) + 2x
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(cos(x - 2) + 2x)`
At x = `2,"dx"/"dy"`
= `((1)/([cos(x - 2) + 2x]))_("at" x = 2)`
= `(1)/(cos0 + 2(2)`
= `(1)/(1 + 4)`
= `(1)/(5)`.
APPEARS IN
संबंधित प्रश्न
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following:
y = `sqrt(x)`
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f-1(y) in the following: y = `sqrt(2 - sqrt(x)`
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f-1(y) in the following: y = `root(3)(x - 2)`
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = 2x + 3
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = e2x-3
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = `log_2(x/2)`
Find the derivative of the inverse function of the following : y = x2·ex
Find the derivative of the inverse function of the following : y = x cos x
Find the derivative of the inverse function of the following : y = x2 + log x
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x5 + 2x3 + 3x, at x = 1
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = ex + 3x + 2
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = 3x2 + 2logx3
If f(x) = x3 + x – 2, find (f–1)'(0).
Using derivative, prove that: tan –1x + cot–1x = `pi/(2)`
Choose the correct option from the given alternatives :
If g is the inverse of function f and f'(x) = `(1)/(1 + x)`, then the value of g'(x) is equal to :
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 18x + log(x - 4).
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25x + log(1 + x2)
If `"x"^3 + "y"^2 + "xy" = 7` Find `"dy"/"dx"`
If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.
Find the derivative of the inverse of function y = 2x3 – 6x and calculate its value at x = −2
Let f(x) = x5 + 2x – 3 find (f−1)'(-3)
Find the derivative of cos−1x w.r. to `sqrt(1 - x^2)`
Choose the correct alternative:
What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x3.
Choose the correct alternative:
What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`
State whether the following statement is True or False:
If y = x2, then the rate of change of demand (x) of a commodity with respect to its price (y) is `1/(2x)`
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2
I.F. of dx = y (x + y ) dy is a function of ______.
The I.F. of differential equation `dy/dx+y/x=x^2-3 "is" log x.`
Find `dy/dx`, if y = `sec^-1((1 + x^2)/(1 - x^2))`.
If y = `cos^-1 sqrt((1 + x^2)/2`, then `dy/dx` = ______.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2
