Help with Derivatives of f(g(h(x))) - I'm Stuck!

[hawkblader]

Homework Statement

Let f(x) = sqrt(sin(e^(x^4*sinx)))

Find f '(x)

I tried this many times and it's really frustrating!

I made it a composition function : f(g(h(x)))

but I'm not getting the answer at all.

At the end, I found :
1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx)

But it's wrong.

Could someone please tell me where I went wrong or how to solve this please.

 

[ehild]

1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx+4*3x^2 sinx)

You left out the blue part.

ehild

 

[hawkblader]

Could you please tell me how you got the blue part?

I put it in and it's still wrong :(

 

[Mark44]

Could you please tell me how you got the blue part?

I put it in and it's still wrong :(

Product rule.

 

[ehild]

1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx)

Sorry, I also was mistaken, the red part is wrong, as you have to apply the product rule on x⁴sinx.

ehild