Find the derivative using the quotient rule $\frac{d}{dx}\left(\ln\left(x^2+\sqrt{x^2+y^2}\right)\right)$

Step-by-step Solution

Go!
Symbolic 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 to the problem

$\frac{2x\sqrt{x^2+y^2}+x}{\sqrt{x^2+y^2}\left(x^2+\sqrt{x^2+y^2}\right)}$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Find the derivative using the quotient rule
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Load more...
Can't find a method? Tell us so we can add it.
1

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{x^2+\sqrt{x^2+y^2}}\frac{d}{dx}\left(x^2+\sqrt{x^2+y^2}\right)$

Learn how to solve problems step by step online.

$\frac{1}{x^2+\sqrt{x^2+y^2}}\frac{d}{dx}\left(x^2+\sqrt{x^2+y^2}\right)$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx(ln(x^2+(x^2+y^2)^(1/2))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final answer to the problem

$\frac{2x\sqrt{x^2+y^2}+x}{\sqrt{x^2+y^2}\left(x^2+\sqrt{x^2+y^2}\right)}$

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

Help us improve with your feedback!

Function Plot

Plotting: $\frac{2x\sqrt{x^2+y^2}+x}{\sqrt{x^2+y^2}\left(x^2+\sqrt{x^2+y^2}\right)}$

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 Personal Math Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account