Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
Advertisements
उत्तर
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
Let y = `sqrt(1 + x^2)`
y = `(1 + x^2)^(1/2)`
Here f(x) = 1 + x2; n = `1/2`
`= 1/2 (1 + x^2)^(1/2 - 1) "d"/"dx" (1 + x^2)`
`= 1/2 (1 + x^2)^(-1/2) (0 + 2x)`
`= 1/2 1/(1 + x^2)^(1/2) (2x)`
`= 1/2 1/sqrt (1 + x^2) (2x)`
`= x/(sqrt (1 + x^2)`
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
x sin x
Differentiate the following with respect to x.
ex sin x
Differentiate the following with respect to x.
(ax2 + bx + c)n
Find `"dy"/"dx"` for the following function.
x2 – xy + y2 = 1
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
Differentiate sin2x with respect to x2.
Find y2 for the following function:
x = a cosθ, y = a sinθ
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If y = tan x, then prove that y2 - 2yy1 = 0.
