Find the derivative of f when...

Question

thatonegirl_ · Answer

$$f(x)=9x^2(4-sinx)^5$$

thatonegirl_ · Answer

Would I use the product rule and the chain rule for this?

nnesha · Answer

yes

tayfishb · Answer

do you know how to product/chain rule it?

thatonegirl_ · Answer

So I'm getting stuck with the (4-sinx)^5

thatonegirl_ · Answer

I'll show what I got so far

thatonegirl_ · Answer

$$18x(4-sinx)^5+9x^2[5(4-sinx)^4\times-cosx]$$

thatonegirl_ · Answer

Is that part right so far?

nnesha · Answer

looks good.

thatonegirl_ · Answer

So how would I simplify that?

thatonegirl_ · Answer

$$9x^2(-5cosx(4-sinx)^4)$$ ???

nnesha · Answer

hmm $$\large\rm 18x (4-sinx)^5+ \color{reD}{9x^2}(5(4-sinx)^4 \cdot -cosx)$$
distribute 2nd term by 9x^2 and then take out the common factor 

$$\large\rm 18x(4-sinx)^5 -45x^2\cos(x) (4-sinx)^4$$

thatonegirl_ · Answer

Oooo thank you!

nnesha · Answer

yw. now just take out the common factor that's it. good job!

thatonegirl_ · Answer

You can only take out (4-sinx)^5 so there's still one (4-sinx) left right?

thatonegirl_ · Answer

Struggling with my algebra xD

nnesha · Answer

would you take out (4-sinx)^5 ??
$$\rm x^5+x^4$$ what is the common factor ??

thatonegirl_ · Answer

x^4

nnesha · Answer

its okay limits derivatives all are easier than algebra for calc students.. :)

thatonegirl_ · Answer

Lol thanks. And i meant x^4 before my b. So there's still another (4-sinx) correct?

nnesha · Answer

yes correct $$x^5+x^4$$
you would take out the variable with the lowest power 
so $$x^4(x+1)$$

thatonegirl_ · Answer

$$(4-sinx)^4[18x(4-sinx)-45x^2cosx)]$$

nnesha · Answer

looks good. what else would be the common factor ?

thatonegirl_ · Answer

9x?

nnesha · Answer

perfect! that's it

thatonegirl_ · Answer

$$9x(4-sinx)^4[2(4-sinx)-5xcosx)]$$

nnesha · Answer

yep

thatonegirl_ · Answer

yayy! Thank you very much!!! <3

nnesha · Answer

yw!