Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
`e^x/(1 + e^x)`
Advertisements
उत्तर
Let y = `e^x/(1 + e^x)`
`"dy"/"dx" = ((1 + e^x) "d"/"dx" (e^x) - e^x "d"/"dx" (1 + e^x))/(1 + e^x)^2`
`= ((1 + e^x) e^x - e^x * e^x)/(1 + e^x)^2`
`= (e^x (1 + e^x - e^x))/(1 + e^x)^2`
`= e^x/(1 + e^x)^2`
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
`sqrtx + 1/root(3)(x) + e^x`
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
(x2 – 3x + 2) (x + 1)
Differentiate the following with respect to x.
x4 – 3 sin x + cos x
Differentiate the following with respect to x.
cos2 x
Differentiate the following with respect to x.
(ax2 + bx + c)n
Differentiate the following with respect to x.
(sin x)x
Differentiate the following with respect to x.
(sin x)tan x
Differentiate sin3x with respect to cos3x.
If y = tan x, then prove that y2 - 2yy1 = 0.
