Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
`e^x/(1 + e^x)`
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.
`e^x/(1 + x)`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
sin x cos x
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
Differentiate the following with respect to x.
sin(x2)
If 4x + 3y = log(4x – 3y), then find `"dy"/"dx"`
If xm . yn = (x + y)m+n, then show that `"dy"/"dx" = y/x`
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
If y = 2 + log x, then show that xy2 + y1 = 0.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
