What is the derivative of $5^tanx$ ?

Question

2921 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-03T10:48:00

$=> (dy)/(dx) = 5^tanx * ln5 * sec^2 x$

We are trying to find $(dy)/(dx)$ when $y = 5^tanx$

Taking natural logs on both sides...

$=> ln y = ln 5^tanx$

Using log laws:

$alpha log beta -= log beta ^ alpha$

$=> ln y =ln5 * tanx$

Differentiating implicitly:

$=> 1/y * (dy)/(dx) = ln5 * sec^2 x$

$=> (dy)/(dx) = y ln5 * sec^2 x$

$=> (dy)/(dx) = 5^tanx * ln5 * sec^2 x$

What is the derivative of 5^tanx5^tanx?