Advertisements
Advertisements
प्रश्न
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Advertisements
उत्तर
We are given
`x^m y^n = (x + y)^(m + n)`
Taking log on both sides, we get
APPEARS IN
संबंधित प्रश्न
if xx+xy+yx=ab, then find `dy/dx`.
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below:
- By using the product rule.
- By expanding the product to obtain a single polynomial.
- By logarithmic differentiation.
Do they all give the same answer?
Find `dy/dx` if y = xx + 5x
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If `log_10((x^3 - y^3)/(x^3 + y^3))` = 2, show that `dy/dx = -(99x^2)/(101y^2)`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.
Differentiate 3x w.r.t. logx3.
Find the nth derivative of the following: log (ax + b)
If y = A cos (log x) + B sin (log x), show that x2y2 + xy1 + y = 0.
If log5 `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
`"d"/"dx" [(cos x)^(log x)]` = ______.
If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.
Derivative of `log_6`x with respect 6x to is ______
`log [log(logx^5)]`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` 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 `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
The derivative of log x with respect to `1/x` is ______.
Find `dy/dx`, if y = (log x)x.
What is \[\frac{1}{y}\cdot\frac{dy}{dx}\] for \[y=\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
Which is the derivative of \[\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
