Question

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

Answer 1

do you know what the chain rule is?

Answer 2

Yes

Answer 3

if\[f(x) = g(h(x))\\f'(x) = g'(h(x))*h'(x)\]

Answer 4

what is the derivative of arctan(x)?

Answer 5

1/(1+x^2)

Answer 6

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
\[f'(x)=\frac{8}{1+(7e^x)^2}*(7e^x)'=\frac{8}{1+49e^{2x}}*7e^x=\frac{56e^x}{1+49e^{2x}}\]

Answer 7

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!!

Answer 8

for sure:)