Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Advertisements
उत्तर
y = etan–1x
y = `"e"^(tan - 1x) (1/(1 + x^2))`
⇒ y’ = `y/(1 + x^2)`
⇒ y'(1 + x2) = y
Differentiating w.r.to x
y’ (2x) + (1 + x2)(y”) = y’
(i.e.) (1 + x2)y” + y’(2x) – y’ = 0
(i.e.) (1 + x2)y” + (2x – 1)y’ = 0
APPEARS IN
संबंधित प्रश्न
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 = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = e–mx
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
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:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
