If f(x) = 8 arctan(7 e^x), find f'( x ). Could sme please tell me the procedure and answer?

Question

zzr0ck3r · Answer

do you know what the chain rule is?

anonymous · Answer

Yes

zzr0ck3r · Answer

if$$f(x) = g(h(x))\f'(x) = g'(h(x))*h'(x)$$

zzr0ck3r · Answer

what is the derivative of arctan(x)?

anonymous · Answer

1/(1+x^2)

zzr0ck3r · Answer

ok
so you have
$$f(x) = 8\arctan(g(x))$$ where g(x) = 7e^x
so
$$f'(x) = 8*\frac{1}{1+g(x)^2}*g'(x) $$
replace g(x) with 7e^x
$$f'(x)=\frac{8}{1+(7e^x)^2}*(7e^x)'=\frac{8}{1+49e^{2x}}*7e^x=\frac{56e^x}{1+49e^{2x}}$$

anonymous · Answer

thank you for your help! I really appreciate it .  I just forgot to distribute the exponent thoroughly. sooner or later, I may post another question!!

zzr0ck3r · Answer

for sure:)