Question

Evaluate the function.

f(x)=5^(ln(x+1))

Answer 1

Is this the complete question?
Is any other information given?

Answer 2

oh whoops. Find f'(0). I know the answer is f'(0)=ln5. But I don't understand the process.

Answer 3

\[f \left( x \right)=5^{\ln \left( x+1 \right)},\ln f \left( x \right)=\ln 5^{\ln \left( x+1 \right)}=\ln \left( x+1 \right)\ln 5\]
diff. w.r.t.x
\[\frac{ f'\left( x \right) }{ f \left( x \right) }=\frac{ \ln 5 }{ x+1 }\]
\[f'\left( x \right)=f \left( x \right)\frac{ \ln 5 }{ x+1 }=5^{\ln \left( x+1 \right)}\frac{ \ln 5 }{ x+1 }\]
i think now you can solve.

Answer 4

Yes, thank you!

Answer 5

you are welcome.

Answer 6

Heyyy Im confused. What does diff. w.r.t.x mean?

Answer 7

with respect to x