Second Derivative of this function Calculate the higher derivative.

f(x) = 5 x sin 5 x

f′′(x) =
I typed in a ton for answers for this problem and still no luck.
Also could not figure out this problem

Question

Second Derivative of this function Calculate the higher derivative. 

f(x) = 5 x sin 5 x 

f′′(x) = 
I typed in a ton for answers for this problem and still no luck.
Also could not figure out this problem

anonymous · Answer

attachment

anonymous · Answer

attachment

anonymous · Answer

Use the product rule. f'(x)=first times derivative of the second + second times derivative of the first.

anonymous · Answer

would f(x)= 5x? or xsin(5x)?

anonymous · Answer

Well, in your original post you state $$f(x)=5x \times \sin (5x)$$

anonymous · Answer

$$f \prime(x)=5x (\cos 5x)\times 5 + \sin5x \times 5$$
Simplified is $$25x \cos5x+5\sin5x$$

anonymous · Answer

oh ok that for the f′′(x) = -125xsin(5x)+25cos(5x)?

anonymous · Answer

*then*

anonymous · Answer

Yes, but don't for get the second part ... the 5sin5x

anonymous · Answer

Should that be an addition to my answer or correcting a part?

anonymous · Answer

In addition to. You found the second derivative of the 25xcos5x, but not the 5sin5x.

anonymous · Answer

so f(x)′′=−125xsin(5x)+25cos(5x)+5sin(5x)

anonymous · Answer

No. The derivatve of 5sin(5x) is 5cos(5x)*5, so 25cos(5x).

anonymous · Answer

f′′(x) = -125xsin(5x)+25cos(5x)+25cos(5x)

anonymous · Answer

Oh wow thanks, to many numbers get me confused lol, did you know how to do any of the attach files by chance?