Posted by **Sunny** on Wednesday, May 1, 2013 at 10:27pm.

Find f’(x) if f(x) = 3^g(x) where g(x) = LOG_3(x^2 - √x + 4/x + 10*LOG_e(x))

- math -
**Reiny**, Wednesday, May 1, 2013 at 10:46pm
if f(x) = 3^g(x)

then f'(x) = (ln3)(3^(gx)) (g ' (x) )

g(x) = ???? , do you mean 3 to be the base of LOG

or are we doing ln ? or what

Once you have decided, continue as below ...

so g ' (x) = ....

insert that result above.

- math -
**Sunny**, Wednesday, May 1, 2013 at 10:55pm
the 3 is the base so log(base3)(...log(base/e)(x)

- math -
**Steve**, Thursday, May 2, 2013 at 12:03pm
if g(u) = log_3(u)

f(x) = 3^g(u) = 3^log_3(u) = u

so now it's easy:

f(x) = x^2 - √x + 4/x + 10*ln(x)

f'(x) = 2x - 1/(2√x) - 4/x^2 + 10/x

## Answer This Question

## Related Questions

- Math - Logarithmic - Solve: 2log_3(x) - log_3(x-2) = 2 My Work: log_3(x^2) - ...
- Math - Find an equation of the line that bisects the obtuse angles formed by the...
- Math - logs - log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * ...
- Math - Could I please get some help for these 3 questions, apologies for asking ...
- 8th grade algebra - Can you check my answers? 1. 3√20/√4 = 3√(...
- Math - Use a sum or difference identity to find the exact value of sin225° a...
- Algebra - How would i complete these problems? 1. (√6mn)^5 2. ^3√16x...
- maths - I will be thankfull to you if you help me to solve the below problem: 6...
- Math - Determine the exact value of cos 465 degrees a) √3 + √2/2 b...
- Algebra Work Check - 1. 5√6 * 1/6√216 5/6 * √1296 5/6 * √...

More Related Questions