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.
(x2 – 3x + 2) (x + 1)
Differentiate the following with respect to x.
ex sin x
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Differentiate sin3x with respect to cos3x.
Differentiate sin2x with respect to x2.
Find y2 for the following function:
y = e3x+2
If y = 2 + log x, then show that xy2 + y1 = 0.
If xy . yx , then prove that `"dy"/"dx" = y/x((x log y - y)/(y log x - x))`
