👉 Try now NerdPal! Our new math app on iOS and Android

Find the derivative $\frac{d}{dx}\left(\frac{\ln\left(x\cos\left(x\right)\right)}{\ln\left(\sqrt{x+1}\right)}\right)$

Step-by-step Solution

Go!
Math mode
Text mode
Go!
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
Dx
|◻|
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

Final Answer

$\frac{\frac{1}{2}\left(x+1\right)\left(\cos\left(x\right)-x\sin\left(x\right)\right)\ln\left(x+1\right)+\frac{1}{2}x\left(-\ln\left(x\right)-\ln\left(\cos\left(x\right)\right)\right)\cos\left(x\right)}{\frac{1}{4}x\left(x+1\right)\ln\left(x+1\right)^2\cos\left(x\right)}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\frac{\ln\left(x\right)+\ln\left(\cos\left(x\right)\right)}{\frac{1}{2}\ln\left(x+1\right)}\right)$

Learn how to solve quotient rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\frac{\ln\left(x\right)+\ln\left(\cos\left(x\right)\right)}{\frac{1}{2}\ln\left(x+1\right)}\right)$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(ln(xcos(x))/ln((x+1)^1/2)). Simplify the derivative by applying the properties of logarithms. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(\ln\left(x\right)+\ln\left(\cos\left(x\right)\right)).

Final Answer

$\frac{\frac{1}{2}\left(x+1\right)\left(\cos\left(x\right)-x\sin\left(x\right)\right)\ln\left(x+1\right)+\frac{1}{2}x\left(-\ln\left(x\right)-\ln\left(\cos\left(x\right)\right)\right)\cos\left(x\right)}{\frac{1}{4}x\left(x+1\right)\ln\left(x+1\right)^2\cos\left(x\right)}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of lnxcosx/ln((x+1)^0.5) using the product ruleFind derivative of lnxcosx/ln((x+1)^0.5) using the quotient ruleFind derivative of lnxcosx/ln((x+1)^0.5) using logarithmic differentiation

Give us your feedback!

Function Plot

Plotting: $\frac{\frac{1}{2}\left(x+1\right)\left(\cos\left(x\right)-x\sin\left(x\right)\right)\ln\left(x+1\right)+\frac{1}{2}x\left(-\ln\left(x\right)-\ln\left(\cos\left(x\right)\right)\right)\cos\left(x\right)}{\frac{1}{4}x\left(x+1\right)\ln\left(x+1\right)^2\cos\left(x\right)}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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
Dx
|◻|
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

How to improve your answer:

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account