Advertisements
Advertisements
Question
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Solution
y = `"e"^((2x + 1))`
Differentiating both sides w.r.t. x, we get
`("d"y)/("d"x) = "e"^((2x + 1))*"d"/("d"x)(2x + 1)`
∴ `("d"y)/("d"x) = "e"^((2x + 1))*(2 + 0)`
∴ `("d"y)/("d"x) = 2"e"^((2x + 1))`
Again, differentiating both sides w.r.t. x , we get
∴ `("d"^2y)/("d"x^2) = 2*"d"/("d"x)"e"^((2x + 1))`
= `2"e"^((2x + 1))*"d"/("d"x)(2x + 1)`
= `2"e"^((2x + 1))*(2 + 0)`
∴ `("d"^2y)/("d"x^2) = 4"e"^((2x + 1))`
RELATED QUESTIONS
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find `"dy"/"dx"` if xey + yex = 1
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
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
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
If y = x10, then `("d"y)/("d"x)` is ______
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
Derivative of ex sin x w.r.t. e-x cos x is ______.
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
y = cos (sin x)
y = sin (ax+ b)
y = `sec (tan sqrt(x))`
y = `2sqrt(cotx^2)`
If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.
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.
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
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)`
Solve the following:
If y = `root5((3x^2 +8x+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)`
If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`
