Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
(sin x)tan x
Advertisements
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.
`e^x/(1 + e^x)`
Differentiate the following with respect to x.
ex sin x
Differentiate the following with respect to x.
cos2 x
Differentiate the following with respect to x.
(ax2 + bx + c)n
Find `"dy"/"dx"` for the following function.
x2 – xy + y2 = 1
Find `"dy"/"dx"` for the following function.
x3 + y3 + 3axy = 1
Find `"dy"/"dx"` of the following function:
x = log t, y = sin t
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
Find y2 for the following function:
x = a cosθ, y = a sinθ
If y = 2 + log x, then show that xy2 + y1 = 0.
