Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Advertisements
उत्तर
`x^2/"a"^2 + y^2/"b"^2` = 1
`(2x)/"a"^2 + (2y)/"b"^2 ("d"y)/("d"x)` = 0
`(2y)/"b"^2 ("d"y)/("d"x) = - (2x)/"a"^2`
`("d"y)/("d"x) = - (2x)/"a"^2 xx "b"^2/(2y)`
`("d"y)/("d"x) = - "b"^2/"a"^2 x/y`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
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
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
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"`
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
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a 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
