Derivative...Chain Rule

(4 + cosx)^6

I see chain rule, do you ?

Question

Derivative...Chain Rule

(4 + cosx)^6

I see chain rule, do you ?

anonymous · Answer

I got 6(4 + cosx)(-sinx)

but I'm missing something! 

@SolomonZelman

anonymous · Answer

@mathaddict4471

anonymous · Answer

@jim_thompson5910

solomonzelman · Answer

$$\frac{d}{dx}(4 + \cos x)^6=6(4 + \cos x)^{6-1}\times (-\sin x),$$

anonymous · Answer

whoops!! the 6-1 ah thank you!

anonymous · Answer

so it would be -6(sinx)(4 +cosx)^5

solomonzelman · Answer

yes

jim_thompson5910 · Answer

Outer function: f(x) = x^6

f ' (x) = 6x^5

Inner function: g(x) = 4+cos(x)

g ' (x) = -sin(x)

Composite function: h(x) = f(g(x)) = [4 + cos(x)]^6

chain rule: h ' (x) = f ' (g(x)) * g ' (x)

but it looks like you already got it

anonymous · Answer

thank you @jim_thompson5910  =) every bit helps !

anonymous · Answer

@SolomonZelman I am terrible at u substition 
Still struggling, what gives ?

solomonzelman · Answer

You just have to understand this: (when f(x) is the inner function)
u = f(x)
du = f'(x) dx

anonymous · Answer

okay I am grasping that part the best 

its just after I find the u and du/dx 
I am lost

anonymous · Answer

i am reading this right now http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/web-integrationbysub-tony.pdf