Find the derivatives of the following: If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0

Find the derivatives of the following:

If y = e^tan–1x, show that (1 + x²)y” + (2x – 1)y’ = 0

योग

y = e^tan–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

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Differentiation Rules

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 24 | पृष्ठ १७६

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 = `tan x/x`

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 = e^-x . log x

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
y = sin²(cos kx)

Differentiate the following:
y = (1 + cos²)⁶

Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`

Differentiate the following:

y = `sin^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:
tan (x + y) + tan (x – y) = x

Find the derivatives of the following:

If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`

Find the derivatives of the following:

sin^-1 (3x – 4x³)

Find the derivatives of the following:

`tan^-1 ((cos x + sin x)/(cos x - sin x))`

Find the derivatives of the following:

Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`