Question #23abc

Question

1103 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-01T21:35:51

$\frac{d f (e^{tan (0)})}{d x} = 5$ $(df(e^tan(0)))/dx = 5$

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

Let $x = 0$ :

$sec^2(0)e^tan(0)f'(e^tan(0))$

Use the fact that $sec^2(0) = 1$ :

$e^tan(0)f'(e^tan(0))$

Use the fact that $tan(0) = 0$ :

$e^0f'(e^0)$

Use the fact that $e^0 = 1$ :

$1f'(1)$

We are given that $f'(1) = 5$

Therefore,

$(df(e^tan(0)))/dx = 5$