Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"`, if x = e3t, y = `"e"^((4"t" + 5))`
Advertisements
उत्तर
x = e3t
Differentiating both sides w.r.t. t, we get
`"dx"/"dt" = "e"^"3t" * (3) = 3 "e"^"3t"`
y = `"e"^(4"t" + 5)`
Differentiating both sides w.r.t. t, we get
`"dy"/"dt" = "e"^((4"t" + 5)) xx 4`
`= 4 * "e"^((4"t" + 5))`
∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt"))`
= `(4 * "e"^(4"t" + 5))/(3* "e"^(3"t"))`
`= 4/3 e^(4"t" + 5 - 3"t")`
`= 4/3 "e"^("t" + 5)`
संबंधित प्रश्न
Find `"dy"/"dx"`, if x = at2, y = 2at
Find `(dy)/(dx)`, if x = 2at2, y = at4.
Find `"dy"/"dx"`, if x = `("u" + 1/"u")^2, "y" = (2)^(("u" + 1/"u"))`
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` = ____.
Choose the correct alternative:
If x = 2am, y = 2am2, where m be the parameter, then `("d"y)/("d"x)` = ?
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"`
State whether the following statement is True or False:
If x = 5m, y = m, where m is parameter, then `("d"y)/("d"x) = 1/5`
If x = `(4"t")/(1 + "t"^2)`, y = `3((1 - "t"^2)/(1 + "t"^2))`, then show that `("d"y)/("d"x) = (-9x)/(4y)`
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")`
Find `dy/dx` if, `x = e^(3t) , y = e^sqrtt`
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))`
If x = f(t) and y = g(t) are differentiable functions of t, so that y is function of x and `(dx)/dt ≠ 0` then prove that `dy/(dx) = (dy/dt)/((dx)/dt)`. Hence find `dy/(dx)`, if x = at2, y = 2at.
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))`
Find `dy/dx if, x= e^(3t)"," y = e^((4t+5))`
