Advertisements
Advertisements
प्रश्न
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Advertisements
उत्तर
y = `"e"^((2"x" + 1))`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "e"^((2"x" + 1)) * "d"/"dx" (2"x" + 1)`
`"dy"/"dx" = "e"^((2"x" + 1)) * (2 + 0)`
`"dy"/"dx" = 2"e"^((2"x" + 1))`
Again, differentiating both sides w.r.t. x, we get
`("d"^2"y")/"dx"^2 = 2 * "d"/"dx" "e"^((2"x" + 1))`
`= 2"e"^((2"x" + 1)) * "d"/"dx" (2"x" + 1)`
`= 2"e"^((2"x" + 1)) * (2 + 0)`
∴ `("d"^2"y")/"dx"^2 = 4"e"^((2"x" + 1))`
APPEARS IN
संबंधित प्रश्न
Find the second order derivative of the function.
x2 + 3x + 2
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"`
Find `("d"^2"y")/"dx"^2`, if y = `sqrt"x"`
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
Derivative of cot x° with respect to x is ____________.
Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p'i(x) and p''i(x) be the first and second order derivatives of pi(x) respectively. Let,
A(x) = `[(p_1(x), p_1^'(x), p_1^('')(x)),(p_2(x), p_2^'(x), p_2^('')(x)),(p_3(x), p_3^'(x), p_3^('')(x))]`
and B(x) = [A(x)]T A(x). Then determinant of B(x) ______
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^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))`
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))`
Find `(d^2y)/dx^2` if, y = `e^(2x +1)`
Find `(d^2y)/dx^2` if, `y = e^((2x+1))`
