Can anyone differentiate??

Question

Please show me how to differentiate these!! I hate cal.


y= sec3 x

y=(x6 sec (x))

y=(x2 cos (x))

Answer 1

for y = [sec x]^3, use chain rule:
y' = 3[sec x]²(sec x tan x)

for y = x^6 sec x use product rule:
y' = 6x^5 (sec x) + x^6 (sec x tan x)

for y = x² cos x also product rule:
y' = 2x cos x - x² sin x

Answer 2

When you differentiate basic trigonometric functions, you use the chain rule:

dy/dx sec(u) = sec(u)tan(u)u' , u = 3x

= 3sec(3x)tan(3x)

For the rest, you must use the product rule:

dy/dx x^6*sec(x), x^6 = v, sec(x) = u

= u'v + uv'

= 6x^5(sec(x)) + x^6(sec(x)tan(x))

dy/dx x^2*cos(x), x^2 = v, cos(x) = u

= u'v + uv'

= 2xcos(x) - x^2(sin(x))

And there you go.