Advertisements
Advertisements
प्रश्न
Find the derivative of cos−1x w.r. to `sqrt(1 - x^2)`
उत्तर
Let u = cos−1x
Differentiating w. r. t. x, we get
`("d"u)/("d"x) = "d"/("d"x)(cos^-1 x)`
= `(-1)/sqrt(1 - x^2)`
Let v = `sqrt(1 - x^2)`
Differentiating w. r. t. x, we get
`("dv")/("d"x) = "d"/("d"x)(sqrt(1 - x^2))`
= `1/(2sqrt(1 - x^2))*"d"/("d"x)(1 - x^2)`
= `1/(2sqrt(1 - x^2))*(-2x)`
= `(-x)/sqrt(1 - x^2)`
∴ `("d"u)/("dv") = (("d"u)/("d"x))/(("dv")/("d"x))`
= `(-1)/((sqrt(1 - x^2))/((-x)/(sqrt(1 - x^2))`
= `1/x`
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 = `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 = ex – 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 function of the following : y = x 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 = sin(x – 2) + x2
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 = 25x + log(1 + x2)
State whether the following is True or False:
If f′ is the derivative of f, then the derivative of the inverse of f is the inverse of f′.
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)` = ______.
If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______
Let f(x) = x5 + 2x – 3 find (f−1)'(-3)
Differentiate `tan^-1[(sqrt(1 + x^2) - 1)/x]` w.r. to `tan^-1[(2x sqrt(1 - x^2))/(1 - 2x^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 = `(3x + 7)/(2x^2 + 5)`
Choose the correct alternative:
If x = at2, y = 2at, then `("d"^2y)/("d"x^2)` = ?
State whether the following statement is True or False:
If y = 10x + 1, then `("d"y)/("d"x)` = 10x.log10
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x2e–x + 2x
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
The I.F. of differential equation `dy/dx+y/x=x^2-3 "is" log x.`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
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
Find the rate of change of demand (x) of a commodity with respect to its price (y) if `y=12+10x+25x^2`
