Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
xsin x
Advertisements
उत्तर
Let y = xsin x
Taking logarithm on both sides we get,
log y = log(xsin x)
log y = sin x log x
Differentiating with respect to x,
`1/y * "dy"/"dx" = sin x "d"/"dx" (log x) + log x "d"/"dx" (sin x)`
`1/y * "dy"/"dx" = sin x (1/x) + log x (cos x)`
`"dy"/"dx" = y[(sin x)/x + cos x log x]`
`therefore "dy"/"dx" = x^(sin x) [(sin x)/x + cos x log x]`
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.
`(3 + 2x - x^2)/x`
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
Differentiate sin3x with respect to cos3x.
Differentiate sin2x with respect to x2.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
If y = sin(log x), then show that x2y2 + xy1 + y = 0.
If y = tan x, then prove that y2 - 2yy1 = 0.
