Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"`, if Differentiate 5x with respect to log x
उत्तर
Let u = 5x and v = log x
u = 5x
Differentiating both sides w.r.t.x, we get
`"du"/"dx" = 5^"x" * log 5`
v = log x
Differentiating both sides w.r.t.x, we get
`"dv"/"dx" = 1/"x"`
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")) = (5^"x" log 5)/(1/"x") = "x"*5^"x" (log 5)`
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`, if x = at2, y = 2at
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 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)`.
Choose the correct alternative.
If x = 2at2 , y = 4at, then `"dy"/"dx" = ?`
If x = `y + 1/y`, then `dy/dx` = ____.
If x sin(a + y) + sin a cos(a + y) = 0 then show that `("d"y)/("d"x) = (sin^2("a" + y))/(sin"a")`
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")`
If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`
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 = 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))`
Find `dy/dx` if, x = `e^(3t)`, y = `e^((4t + 5))`.
