Advertisements
Advertisements
प्रश्न
Solve the following.
If x = `"a"(1 - 1/"t"), "y" = "a"(1 + 1/"t")`, then show that `"dy"/"dx" = - 1`
Advertisements
उत्तर
x = `"a"(1 - 1/"t")`
Differentiating both sides w.r.t. ‘t’, we get
`"dx"/"dt" = "a"[0 - ((-1)/"t"^2)] = "a"/"t"^2`
y = `"a"(1 + 1/"t")`
Differentiating both sides w.r.t. ‘t’, we get
`"dy"/"dt" = "a"[0 + ((-1)/"t"^2)] = "-a"/"t"^2`
∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")) = ("-a"/"t"^2)/("a"/"t"^2)` = - 1
APPEARS IN
संबंधित प्रश्न
Find `(dy)/(dx)`, if x = 2at2, y = at4.
Find `"dy"/"dx"`, if x = e3t, y = `"e"^((4"t" + 5))`
Find `"dy"/"dx"`, if x = `("u" + 1/"u")^2, "y" = (2)^(("u" + 1/"u"))`
Find `"dy"/"dx"`, if Differentiate 5x with respect to log x
If x = t . log t, y = tt, then show that `dy/dx - y = 0`.
If x = 2at2 , y = 4at, then `dy/dx = ?`
If x = `y + 1/y`, then `dy/dx` = ____.
Find `"dy"/"dx"` if x = 5t2, y = 10t.
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)`
If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`
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
Suppose y = f(x) is differentiable function of x and y is one-one onto, `dy/dx ≠ 0`. Also, if x = f–1(y) is differentiable, then prove that `dx/dy = 1/((dy/dx))`, where `dy/dx ≠ 0`
Hence, find `d/dx(tan^-1x)`.
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 ^(3^t), 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))`.
