Advertisements
Advertisements
प्रश्न
If y = cos−1 [sin (4x)], find `("d"y)/("d"x)`
Advertisements
उत्तर
y = cos−1 [sin (4x)]
= `cos^-1 [cos(pi/2 - 4^x)]`
= y = `pi/2 - 4^x`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)(pi/2 - 4^x)`
= 0 – 4x log 4
= – 4x log 4
APPEARS IN
संबंधित प्रश्न
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Find `"dy"/"dx"` if xey + yex = 1
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find the second order derivatives of the following : e4x. cos 5x
Find `dy/dx` if, y = `sqrt(x + 1/x)`
Find `"dy"/"dx"` if, y = (5x3 - 4x2 - 8x)9
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
The derivative of f(x) = ax, where a is constant is x.ax-1.
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
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
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
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))`
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)`
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If f(x) = |cos x|, find f'`((3pi)/4)`
y = `sec (tan sqrt(x))`
y = `2sqrt(cotx^2)`
y = `cos sqrt(x)`
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
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 `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
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`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.
If y = `log((x + sqrt(x^2 + a^2))/(sqrt(x^2 + a^2) - x))`, find `dy/dx`.
Find `dy/dx` if, y = `e^(5x^2 -2x + 4)`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 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`
