Question

1) F(x)=4^xlog(small=>)7(x)]
2) f(x)=[Inx]^4
3)f(x)=2x^(4x)
4)f(x)=In(sqrt(6x+7)(7x-3))

Answer 1

@wio

Answer 2

Okay, what's difficult?

Answer 3

Logarithmic Derivatives!

Answer 4

\[
(\ln(F(x)))' = \frac{F'(x)}{F(x)}
\]

Answer 5

You want to take the logarithm of both sides, simplify things, and then implicitly differentiate.

Answer 6

how do i do that? :O

Answer 7

Is this correct?\[
F(x)=4^x\log_7(x)
\]

Answer 8

yes, thars right!

Answer 9

There is no need to do this one with logarithmic differentiation, it'd be easier to do product rule.

Answer 10

yea i was told by someone that but my teacher want me to do it by using Logarithmic Derivatives rules

Answer 11

could you teach me please?

Answer 12

\[
\ln[F(x)]=\ln[4^x\log_7(x)] = x\ln(4)+\ln[\log_7(x)]
\]Differentiate both sides: \[
\frac{F'(x)}{F(x)} = \ln(4) + \frac{\frac{1}{x\ln(7)}}{\log_7(x)}
\]

Answer 13

Put back in the value for \(F(x)\)\[
\frac{F'(x)}{4^x\log_7(x)} = \ln(4) + \frac{\frac{1}{x\ln(7)}}{\log_7(x)}
\]Simplify a bit: \[
F'(x) = 4^x\log_7(x)\ln(4) + \frac{4^x}{x\ln(7)}
\]

Answer 14

thats really cool how you solve the problem easily. the last sentence is the answer ?

Answer 15

I showed every step...

Answer 16

thank you. !

Answer 17

how do the next question?

Answer 18

One question per help.

Answer 19

you wont help me?