Advertisements
Advertisements
प्रश्न
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
उत्तर
Let u = log(1 + x2) and v = tan-1 (x)
Deffrentiating both sides with respect to x.
`(du)/dx = 1/(1 + x^2) . 2x, (dv)/dx = 1/(1 + x^2)`
`(du)/(dv) = ((du)/dx)/((dv)/dx) = ((2x/1 + x^2))/((1/(1 + x^2))`
`(du)/(dv) = 2x`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
`x^(xcosx) + (x^2 + 1)/(x^2 -1)`
Find `dy/dx`for the function given in the question:
xy + yx = 1
If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Evaluate
`int 1/(16 - 9x^2) dx`
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
If x = `(2bt)/(1 + t^2), y = a((1 - t^2)/(1 + t^2)), "show that" "dx"/"dy" = -(b^2y)/(a^2x)`.
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
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`
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
If `"y" = "e"^(1/2log (1 + "tan"^2"x")), "then" "dy"/"dx"` is equal to ____________.
