Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
cos2 x
Advertisements
उत्तर
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
y = cos2 x = (cos x)2
`"dy"/"dx" = 2 (cos x)^(2 - 1) "d"/"dx" (cos x)`
= 2 cos x (-sin x)
= -2 sin x cos x
= -sin 2x
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
3x4 – 2x3 + x + 8
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
sin x cos x
Differentiate the following with respect to x.
sin(x2)
Differentiate the following with respect to x.
xsin x
Find `"dy"/"dx"` of the following function:
x = log t, y = sin t
Differentiate sin3x with respect to cos3x.
Find y2 for the following function:
y = log x + ax
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
If y = tan x, then prove that y2 - 2yy1 = 0.
