Advertisements
Advertisements
Question
Differentiate the following with respect to x.
`e^x/(1 + x)`
Advertisements
Solution
Let y = `e^x/(1 + x)`
`"dy"/"dx" = (1 + x "d"/"dx" (e^x) - e^x "d"/"dx" (1 + x))/(1 + x)^2`
`= ((1 + x)e^x - e^x * 1)/(1 + x)^2`
`= (e^x (1 + x - 1))/(1 + x)^2`
`= (xe^x)/(1 + x)^2`
APPEARS IN
RELATED QUESTIONS
Differentiate the following with respect to x.
`(3 + 2x - x^2)/x`
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
Differentiate the following with respect to x.
(ax2 + bx + c)n
Find `"dy"/"dx"` for the following function.
x3 + y3 + 3axy = 1
Differentiate the following with respect to x.
xsin x
Differentiate sin3x with respect to cos3x.
Find y2 for the following function:
y = log x + ax
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x2) y2 + xy1 – m2y = 0
If y = sin(log x), then show that x2y2 + xy1 + y = 0.
