Advertisements
Advertisements
प्रश्न
If y = sin(log x), then show that x2y2 + xy1 + y = 0.
Advertisements
उत्तर
y = sin(log x)
y1 = cos(log x) `"d"/"dx"` (log x)
y1 = cos(log x) . `1/x`
∴ xy1 = cos(log x)
Differentiating both sides with respect to x, we get
xy2 + y1(1) = -sin(log x) . \[\frac{1}{x}\]
⇒ x[xy2 + y1] = -sin(log x)
⇒ x2y2 + xy1 = -y
⇒ x2y2 + xy1 + y = 0
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
3x4 – 2x3 + x + 8
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
`e^x/(1 + x)`
Differentiate the following with respect to x.
`1/sqrt(1 + x^2)`
Differentiate the following with respect to x.
(sin x)tan x
Differentiate sin2x with respect to x2.
Find y2 for the following function:
y = log x + ax
Find y2 for the following function:
x = a cosθ, y = a sinθ
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x2) y2 + xy1 – m2y = 0
