Advertisements
Advertisements
प्रश्न
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Advertisements
उत्तर
y = `"e"^"log x"`
y = x
Differentiating both sides w.r.t.x, we get
`d/dx` (y) = `d/dx` (x)
`"dy"/"dx" = 1`
Again, by differentiating both sides w.r.t.x, we get
`d/dx (dy/dx)` = `d/dx(1)`
`("d"^2"y")/"dx"^2 = 0`
APPEARS IN
संबंधित प्रश्न
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
sin (log x)
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
If x7 . y9 = (x + y)16 then show that `"dy"/"dx" = "y"/"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
sec(x + y) = xy
tan–1(x2 + y2) = a
If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
Derivative of cot x° with respect to x is ____________.
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
Find `(d^2y)/dx^2 "if," y= e^((2x+1))`
Find `(d^2y)/dx^2` if, y = `e^(2x +1)`
Let \[y=f(x)\]. What is the first derivative of \[y\] with respect to \[x\]?
Which expression defines the second order derivative of \[y\] with respect to \[x\]?
Which of the following is NOT a stated notation for the second derivative of \[f(x)\]?
If \[y=\sin^{-1}x\], what is \[\frac{dy}{dx}\]?
Which equation is equivalent to \[\frac{dy}{dx}=\frac{1}{\sqrt{1-x^2}}\] for \[y=\sin^{-1}x\]?
What is \[\frac{d}{dx}\left(\sqrt{1-x^2}\right)\] in the differentiation for \[y=\sin^{-1}x\]?
