Advertisements
Advertisements
प्रश्न
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
उत्तर
`log_5((x^4 + y^4)/(x^4 - y^4))` = 2
`(x^4 + y^4)/(x^4 - y^4)` = 52
`(x^4 + y^4)/(x^4 - y^4)` = 25
`(x^4 + y^4)/(x^4 - y^4)` = 25
x4 + y4 = 25(x4 – y)4
x4 + y4 = 25x4 – 25y4
∴ y4 + 25y4 = 25x4 − x4
26y4 = 24x4
Differentiating both sides w.r.t.x, we get
`26d/dxy^4 = 24"d"/"dx"x^4`
`26. 4y^3 dy/dx = 24. 4x^3 d/dx x`
`26y^3 dy/dx = 24x^3`
`dy/dx = (24x^3)/(26y^3)`
`dy/dx = (12x^3)/(13y^3)`
Notes
The question is modified.
APPEARS IN
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
`(x cos x)^x + (x sin x)^(1/x)`
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Find `(d^2y)/(dx^2)` , if y = log x
If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.
If `log_10((x^3 - y^3)/(x^3 + y^3)) = 2, "show that" "dy"/"dx" = -(99x^2)/(101y^2)`
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
Find the second order derivatives of the following : x3.logx
Find the nth derivative of the following : log (2x + 3)
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
If x7 . y5 = (x + y)12, show that `("d"y)/("d"x) = y/x`
If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?
The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 1 O min, then the time required to drop the temperature upto 295 K.
Derivative of loge2 (logx) with respect to x is _______.
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`d/dx(x^{sinx})` = ______
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
Derivative of `log_6`x with respect 6x to is ______
`2^(cos^(2_x)`
`log (x + sqrt(x^2 + "a"))`
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.
If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`, then `f^'(1)` is equal to
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
Evaluate:
`int log x dx`
If xy = yx, then find `dy/dx`
