Advertisements
Advertisements
Question
y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`
Solution: Given,
y = (6x4 – 5x3 + 2x + 3)6
Let u = `[6x^4 - 5x^3 + square + 3]`
∴ y = `"u"^square`
∴ `("d"y)/"du"` = 6u6–1
∴ `("d"y)/"du"` = 6( )5
and `"du"/("d"x) = 24x^3 - 15(square) + 2`
By chain rule,
`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`
∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`
Advertisements
Solution
Given,
y = (6x4 – 5x3 + 2x + 3)6
Let u = [6x4 – 5x3 + 2x + 3]
∴ y = `"u"^6`
∴ `("d"y)/"du"` = 6u6–1
∴ `("d"y)/"du"` = 6(u)5
and `"du"/("d"x) = 24x^3 - 15x^2 + 2`
By chain rule,
`("d"y)/("d"x) = ("d"y)/"du" xx "du"/("d"x)`
∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^5 xx (24x^3 - 15x^2 + 2)`
APPEARS IN
RELATED QUESTIONS
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find `dy/dx` if, y = `sqrt(x + 1/x)`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Fill in the Blank.
If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.
State whether the following is True or False:
The derivative of polynomial is polynomial.
Find `"dy"/"dx"`, if y = xx.
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
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If f(x) = |cos x|, find f'`((3pi)/4)`
y = `sec (tan sqrt(x))`
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 ______.
Find `"dy"/"dx"` if, `"y" = "e"^(5"x"^2 - 2"x" + 4)`
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)`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
