Advertisements
Advertisements
Question
Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`
Advertisements
Solution
y = `"x"^-7`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = -7"x"^-8`
Again, differentiating both sides w.r.t. x , we get
`("d"^2"y")/"dx"^2 = -7 * "d"/"dx" ("x"^-8)`
`= - 7(-8)"x"^-9`
∴ `("d"^2"y")/"dx"^2 = 56"x"^-9`
APPEARS IN
RELATED QUESTIONS
If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`
Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`
If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`
Find the second order derivative of the function.
x2 + 3x + 2
Find the second order derivative of the function.
x . cos x
Find the second order derivative of the function.
log x
Find the second order derivative of the function.
x3 log x
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
sin (log x)
If y = cos–1 x, find `(d^2y)/dx^2` in terms of y alone.
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"`
If `x^3y^5 = (x + y)^8` , 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))`.
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
`"Find" (d^2y)/(dx^2) "if" y=e^((2x+1))`
Find `(d^2y)/dx^2 if, y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, y = `e^(2x +1)`
If y = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
Find `(d^2y)/dx^2, "if" y = e^((2x+1))`
Find `(d^2y)/dx^2` if, `y = e^((2x+1))`
