Advertisements
Advertisements
Question
State whether the following statement is True or False:
If y = ex, then `("d"^2y)/("d"x^2)` = ex
Options
True
False
Solution
True
APPEARS IN
RELATED QUESTIONS
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find the second order derivatives of the following : xx
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
The derivative of f(x) = ax, where a is constant is x.ax-1.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
If y = cos−1 [sin (4x)], find `("d"y)/("d"x)`
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If `sqrt(1 - x^2) + sqrt(1 - y^2) = "a"(x - y)`, prove that `"dy"/"dx" = sqrt((1 - y^2)/(1 - x^2)`
Let x(t) = `2sqrt(2) cost sqrt(sin2t)` and y(t) = `2sqrt(2) sint sqrt(sin2t), t ∈ (0, π/2)`. Then `(1 + (dy/dx)^2)/((d^2y)/(dx^2)` at t = `π/4` is equal to ______.
If f(x) = `{{:(x^3 + 1",", x < 0),(x^2 + 1",", x ≥ 0):}`, g(x) = `{{:((x - 1)^(1//3)",", x < 1),((x - 1)^(1//2)",", x ≥ 1):}`, then (gof) (x) is equal to ______.
If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.
Solve the following:
If`y=root(5)((3x^2+8x+5)^4),"find" (dy)/dx`
The differential equation of (x - a)2 + y2 = a2 is ______
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If x = Φ(t) is a differentiable function of t, then prove that:
`int f(x)dx = int f[Φ(t)]*Φ^'(t)dt`
Hence, find `int(logx)^n/x dx`.
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.