Question

Hello, I really need help on these two homework problem. ><

In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well?

I would like a step by step process and explanation on how to solve these functions. I cannot seem to understand how to go about them correctly..

I would greatly appreciate it.
Thank you.

1) Solve the equation:

75/(16e^0.2x) = 30


2)Differentiate the function:

h(x) = 8^tanx

Answer 1

e^.2x = 75/(30*16)

.2x ln e = ln (75/480)
but ln e = 1
.2 x = ln (75/480)
=======================
8^tan x * ln 8 * (1/sec^2 x)

Answer 2

Thank you so much.

Although for problem number 1, I realized that I inputted it incorrectly (having problems with my + key).

It is actually:
75/(1+6e^0.2x) = 30

Would I still solve it the same way but subtract 1 to the other side?

Answer 3

make that sec^2 x and not 1/sec^2 x