Advertisements
Advertisements
Question
Differentiate the following with respect to x.
`1/sqrt(1 + x^2)`
Advertisements
Solution
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 = `1/sqrt(1 + x^2)`
y = `(1 + x^2)^(- 1/2)`
Here n = `- 1/2`; f(x) = 1 + x2
`"dy"/"dx" = - 1/2(1 + x^2)^(- 1/2 - 1) "d"/"dx" (1 + x^2)`
`= - 1/2 (1 + x^2)^(- 3/2)`(0 + 2x)
`= - 1/2 1/(1 + x^2)^(3/2)`(2x)
`= - x/(sqrt (1 + x^2))^3`
`= (-x)/(sqrt((x + x^2)^2) sqrt(1 + x^2))`
`= (-x)/((1 + x^2)sqrt(1 + x^2))`
APPEARS IN
RELATED QUESTIONS
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
sin x cos x
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
(ax2 + bx + c)n
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Find `"dy"/"dx"` of the following function:
x = log t, y = sin t
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
