Advertisements
Advertisements
प्रश्न
Differentiate `"e"^("4x" + 5)` with respect to 104x.
Advertisements
उत्तर
Let u = `"e"^(("4x" + 5))` and v = 104x.
u = `"e"^(("4x" + 5))`
Differentiating both sides w.r.t.x, we get
`"du"/"dx" = "e"^(("4x" + 5)) * "d"/"dx" (4"x" + 5)`
`= "e"^(("4x" + 5)) * (4 + 0)`
∴ `"du"/"dx" = 4 * "e"^(("4x" + 5)) *`
v = 104x
Differentiating both sides w.r.t.x, we get
`"dv"/"dx" = 10^"4x" * log 10 * "d"/"dx" ("4x")`
∴ `"dv"/"dx" = 10^"4x" * (log 10) (4)`
∴ `"du"/"dv" = ("du"/"dx")/("dv"/"dx") = (4 * "e"^(("4x" + 5)))/(10^"4x" * (log 10)(4))`
∴ `"du"/"dv" = ("e"^(("4x" + 5)))/(10^"4x" * (log 10)`
APPEARS IN
संबंधित प्रश्न
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
If y = log (cos ex) then find `"dy"/"dx".`
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
`d/dx(10^x) = x*10^(x - 1)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
Find `"dy"/"dx"`, if y = xx.
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)` = ______
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
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 – sinx|, find `"f'"(pi/6)`
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| 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.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
The differential equation of (x - a)2 + y2 = a2 is ______
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
lf 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 prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
If f(x) = `sqrt(7*g(x) - 3)`, g(3) = 4 and g'(3) = 5, find f'(3).
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
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 `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
