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

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Final answer to the problem

$\frac{1}{2x}$
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  • 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
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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 $\displaystyle f'(x)=\frac{a'}{a}$

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(ln((x^(1/2))/(y+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}. Divide fractions \frac{1}{\frac{\sqrt{x}}{y+2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. The derivative of a function multiplied by a constant (\frac{1}{y+2}) is equal to the constant times the derivative of the function. Multiplying fractions \frac{y+2}{\sqrt{x}} \times \frac{1}{y+2}.

Final answer to the problem

$\frac{1}{2x}$

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Plotting: $\frac{1}{2x}$

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0
a
b
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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:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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