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.
`(3 + 2x - x^2)/x`
Differentiate the following with respect to x.
(x2 – 3x + 2) (x + 1)
Differentiate the following with respect to x.
x4 – 3 sin x + cos x
Differentiate the following with respect to x.
ex (x + log x)
Differentiate the following with respect to x.
(ax2 + bx + c)n
Differentiate the following with respect to x.
sin(x2)
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Find `"dy"/"dx"` for the following function.
x3 + y3 + 3axy = 1
If `xsqrt(1 + y) + ysqrt(1 + x)` = 0 and x ≠ y, then prove that `"dy"/"dx" = - 1/(x + 1)^2`
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
