Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
(sin x)tan x
उत्तर
Let y = (sin x)tan x
Taking logarithm on both sides we get,
log y = tan x log(sin x)
Differentiating with respect to x,
`1/y "dy"/"dx" = tan x "d"/"dx"` (log (sin x)) + log (sin x) `"d"/"dx"` (tan x)
= tan x `1/(sin x)`(cos x) + log (sin x) sec2x
`1/y "dy"/"dx" = (sin x)/(cos x) xx (cos x)/(sin x)` + log (sin x)(sec2x)
= 1 + log (sin x)(sec2x)
`"dy"/"dx"` = y[1 + sec2x log (sin x)]
= (sin x)tan x[1 + sec2x log (sin x)]
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
3x4 – 2x3 + x + 8
Differentiate the following with respect to x.
x4 – 3 sin x + cos x
Differentiate the following with respect to x.
`e^x/(1 + e^x)`
Differentiate the following with respect to x.
sin x cos x
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
(ax2 + bx + c)n
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Find `"dy"/"dx"` for the following function.
x2 – xy + y2 = 1
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Find y2 for the following function:
y = e3x+2
