Advertisements
Advertisements
Question
If x = 2at2 , y = 4at, then `dy/dx = ?`
Options
`- 1/(2at^2)`
`1/(2at^3)`
`1/t`
`1/(4at^3)`
Advertisements
Solution
`bb(1/t)`
Explanation:
x = 2at2 , y = 4at
∴ `dx/dt = 2a(2t) and dy/dx = 4a`
∴ `dx/dt = 4at and dy/dt = 4a`
∴ `dy/dx = (dy/dt)/(dx/dt) = (4a)/(4at) = 1/t`
RELATED QUESTIONS
Find `(dy)/(dx)`, if x = 2at2, y = at4.
Find `"dy"/"dx"`, if x = e3t, y = `"e"^((4"t" + 5))`
Find `"dy"/"dx"`, if x = `sqrt(1 + "u"^2), "y" = log (1 + "u"^2)`
If x = `(4t)/(1 + t^2), y = 3((1 - t^2)/(1 + t^2))` then show that `dy/dx = (-9x)/(4y)`.
If x = t . log t, y = tt, then show that `dy/dx - y = 0`.
If x = `y + 1/y`, then `dy/dx` = ____.
Find `"dy"/"dx"` if x = 5t2, y = 10t.
If x = `"a"("t" - 1/"t")`, y = `"a"("t" + 1/"t")`, where t be the parameter, then `("d"y)/("d"x)` = ?
State whether the following statement is True or False:
If x = 2at, y = 2a, where t is parameter, then `("d"y)/("d"x) = 1/"t"`
Find `("d"y)/("d"x)`, if x = em, y = `"e"^(sqrt("m"))`
Solution: Given, x = em and y = `"e"^(sqrt("m"))`
Now, y = `"e"^(sqrt("m"))`
Diff.w.r.to m,
`("d"y)/"dm" = "e"^(sqrt("m"))("d"square)/"dm"`
∴ `("d"y)/"dm" = "e"^(sqrt("m"))*1/(2sqrt("m"))` .....(i)
Now, x = em
Diff.w.r.to m,
`("d"x)/"dm" = square` .....(ii)
Now, `("d"y)/("d"x) = (("d"y)/("d"m))/square`
∴ `("d"y)/("d"x) = (("e"sqrt("m"))/square)/("e"^"m")`
∴ `("d"y)/("d"x) = ("e"^(sqrt("m")))/(2sqrt("m")*"e"^("m")`
If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`
Find `dy/dx` if, x = e3t, y = `e^((4t + 5))`
If x = f(t) and y = g(t) are differentiable functions of t, then prove that:
`dy/dx = ((dy//dt))/((dx//dt))`, if `dx/dt ≠ 0`
Hence, find `dy/dx` if x = a cot θ, y = b cosec θ.
Find the derivative of 7x w.r.t.x7
Find `dy/dx` if, x = e3t, y = `e^((4t+5))`
Find `dy/dx` if, x = `e^(3t)`, y = `e^(4t+5)`
Find `dy/dx if, x = e^(3t),y=e^((4t+5))`
Find `dy/dx` if, `x=e^(3t), y=e^((4t+5))`
Find `dy/dx if,x = e^(3^T), y = e^((4t + 5)`
Find `dy/dx` if, `x = e^(3t), y = e^((4t + 5))`
