Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Advertisements
उत्तर
y = `(cos^-1 x)^2`
`("d"y)/("d"x) = 2(cos^-1_x) xx 1/(- sqrt(1 - x^2)`
`sqrt(1 - x^2) ("d"y)/("d"x) = - 2 cos^-1 x`
`sqrt(1 - x^2) * ("d"^2y)/("d"x)^2 + ("d"y)/("d"x) xx 1/2 (1 - x^2)^(1/2 - 1) (- 2x) = - 2xx 1/sqrt(1 - x^2)`
`sqrt(1 - x^2) ("d"^2y)/("d"x^2) - x (1 - x^2)^(1/2) ("d"y)/("d"x) = 2/sqrt(1 - x^2)`
`sqrt(1 - x^2) ("d"^2y)/("d"x^2) - x/sqrt(1 - x^2) ("d"y)/("d"x) = 2/sqrt(1 - x^2)`
`sqrt(1 - x^2) [sqrt(1 - x^2) ("d"^2y)/("d"x) - x/sqrt(1 - x^2) ("d"y)/("d"x)]` = 2
`(1 - x^2) ("d"^2y)/("d"x^2) - x * ("d"y)/("d"x)` = 2
`(1 - x^2) ("d"^2y)/("d"x^2) - x ("d"y)/("d"x) - 2` = 0
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = sin (ex)
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
