Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
(sin x)x
Advertisements
उत्तर
Let y = (sin x)x
Taking logarithm on both sides we get,
log y = x log(sin x)
Differentiating with respect to x,
`1/y * "dy"/"dx" = x "d"/"dx" log(sin x) + log(sin x) "d"/"dx" (x)`
`1/y * "dy"/"dx" = x1/(sin x) (cos x) + log(sin x)(1)`
`1/y * "dy"/"dx"` = x cot x + log(sin x)
`"dy"/"dx"` = y[x cot x + log(sin x)]
`"dy"/"dx"`= (sin x)x [x cot x + log(sin 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.
`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.
`e^x/(1 + e^x)`
Differentiate the following with respect to x.
cos2 x
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
Differentiate the following with respect to x.
xsin x
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
