How do you differentiate $f(x)=e^(secsqrtx)$ using the chain rule.?

Question

1566 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-11T00:26:44

$f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)$

According to the chain rule,

$f'(x)=e^(secsqrtx)d/dx[secsqrtx]$

First, find the internal derivative (again using the chain rule).

$d/dx[secsqrtx]=secsqrtxtansqrtxd/dx[sqrtx]$

$=1/2x^(-1/2)secsqrtxtansqrtx$

$=(secsqrtxtansqrtx)/(2sqrtx)$

Plug this back in to find $f'(x)$ .

$f'(x)=(e^(secsqrtx))(secsqrtxtansqrtx)/(2sqrtx)$

$f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)$

How do you differentiate f(x)=e^(secsqrtx)f(x)=e^(secsqrtx) using the chain rule.?