Advertisements
Advertisements
प्रश्न
Find the second order derivatives of the following : e4x. cos 5x
Advertisements
उत्तर
Let y = e4x. cos 5x
Then `"dy"/"dx" = "d"/"dx"(e^(4x).cos5x)`
= `e^(4x)."d"/"dx"(cos5x) + cos5x."d"/"dx"(e^(4x))`
= `e^(4x).(-sin5x)."d"/"dx"(5x) + cos5x xx e^(4x)."d"/"dx"(4x)`
= – e4x . sin 5x × 5 + e4x cos 5x × 4
= e4x (4 cos 5x – 5 sin 5x)
and `(d^2y)/(dx^2) = "d"/"dx"[e^(4x)(4cos5x - 5sin5x)]`
`= e^(4x)"d"/"dx"(4cos5x - 5sin5x) + (4cos5x - 5sin5x)."d"/"dx"(e^(4x))`
`= e^(4x)[4 (- sin 5x)."d"/"dx"(5x) - 5cos5x."d"/"dx"(5x)] + (4cos5x - 5sin5x) xx e^(4x)."d"/"dx"(4x)`
= e4x [– 4 sin 5x × 5 – 5 cos 5x × 5] + (4 cos 5x – 5 sin 5x) e4x × 4
= e4x(– 20 sin 5x – 25 cos 5x + 16 cos 5x – 20 sin 5x)
= e4x (– 9 cos 5x – 40 sin 5x)
= – e4x (9 cos 5x + 40 sin 5x)
संबंधित प्रश्न
If y = log (cos ex) then find `"dy"/"dx".`
Find `dy/dx`, if `sqrt(x) + sqrt(y) = sqrt(a)`.
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find the second order derivatives of the following : e2x . tan x
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
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.
State whether the following is True or False:
The derivative of polynomial is polynomial.
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x such that the composite function y = f[g(x)] is a differentiable function of x, then `("d"y)/("d"x) = ("d"y)/("d"u)*("d"u)/("d"x)`. Hence find `("d"y)/("d"x)` if y = sin2x
If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable function of x and `(dx)/(dt)` ≠ 0 then `(dy)/(dx) = ((dy)/(dt))/((dx)/(d"))`.
Hence find `(dy)/(dx)` if x = sin t and y = cost
State whether the following statement is True or False:
If y = ex, then `("d"^2y)/("d"x^2)` = ex
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If y = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
y = sin (ax+ b)
Let f(x) = x | x | and g(x) = sin x
Statement I gof is differentiable at x = 0 and its derivative is continuous at that point.
Statement II gof is twice differentiable at x = 0.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If `y = root5(3x^2 + 8x + 5)^4`, find `dy/dx`
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
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`.
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
