Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\left(1+x\right)^{\frac{1}{x}}\right)$

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Solving: $\frac{d}{dx}\left(\left(1+x\right)^{\frac{1}{x}}\right)$

Solve instead: $\frac{dy}{dx}\left(\left(1+x\right)^{\frac{1}{x}}\right)$

 Solution

 Videos

Pre-Calculus - Condensing a logarithmic expression to one logarithm 2[3lnx - ln(x+1)-ln(x-1)]

https://www.youtube.com/watch?v=HS0--oEAT4I

 Function Plot

Plotting: $\frac{\left(x-\ln\left(1+x\right)-x\ln\left(1+x\right)\right)\left(1+x\right)^{\left(\frac{1}{x}-1\right)}}{x^2}$

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1

2

3

4

5

6

7

8

9

0



a

b

c

d

f

g

m

n

u

v

w

x

y

z

.

(◻)

+

-

×

◻/◻

/

÷

◻²

◻^◻

√◻

√

^◻√◻

^◻√

∞

e

π

ln

log

log_◻

lim

d/dx

D^□_x

∫

∫^◻

|◻|

θ

=

>

<

>=

<=

sin

cos

tan

cot

sec

csc

asin

acos

atan

acot

asec

acsc

sinh

cosh

tanh

coth

sech

csch

asinh

acosh

atanh

acoth

asech

acsch

Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\left(1+x\right)^{\frac{1}{x}}\right)$

Related Videos

 Solution

 Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

How to take the derivative using chain rule with natural log and cosine

Use the product rule to take the derivative of an exponential equation

Use the quotient rule to take the derivative of a natural logarithm

Taking the derivative of a exponential equation using the quotient rule

Pre-Calculus - Condensing a logarithmic expression to one logarithm 2[3lnx - ln(x+1)-ln(x-1)]

 Function Plot

Plotting: $\frac{\left(x-\ln\left(1+x\right)-x\ln\left(1+x\right)\right)\left(1+x\right)^{\left(\frac{1}{x}-1\right)}}{x^2}$

beta
Got a different answer? Verify it!

 How to improve your answer:

 Main Topic: Simplification of algebraic expressions

 Related Topics

Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\left(1+x\right)^{\frac{1}{x}}\right)$

Related Videos

 Solution

 Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

How to take the derivative using chain rule with natural log and cosine

Use the product rule to take the derivative of an exponential equation

Use the quotient rule to take the derivative of a natural logarithm

Taking the derivative of a exponential equation using the quotient rule

Pre-Calculus - Condensing a logarithmic expression to one logarithm 2[3lnx - ln(x+1)-ln(x-1)]

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 Function Plot

Plotting: $\frac{\left(x-\ln\left(1+x\right)-x\ln\left(1+x\right)\right)\left(1+x\right)^{\left(\frac{1}{x}-1\right)}}{x^2}$

beta Got a different answer? Verify it!

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 Main Topic: Simplification of algebraic expressions

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