Advertisements
Advertisements
Question
Differentiate the following with respect to x.
cos3 x
Advertisements
Solution
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 = cos3 x
y = (cos x)3
`"dy"/"dx" = 3(cos x)^(3-1) "d"/"dx" (cos x)`
= 3 cos2 x (-sin x)
= -3 cos2 x sin x
= -3 cos x (sin x cos x) [Multiply and divide by 2]
= `(-3)/2` cos x (2 sin x cos x)
= `(-3)/2` cos x sin 2x
APPEARS IN
RELATED QUESTIONS
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.
`sqrt(1 + x^2)`
Find `"dy"/"dx"` for the following function
xy – tan(xy)
If xm . yn = (x + y)m+n, then show that `"dy"/"dx" = y/x`
Differentiate sin3x with respect to cos3x.
If y = 2 + log x, then show that xy2 + y1 = 0.
If = a cos mx + b sin mx, then show that y2 + m2y = 0.
If xy2 = 1, then prove that `2 "dy"/"dx" + y^3`= 0
If y = tan x, then prove that y2 - 2yy1 = 0.
