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# Find the derivative of $x\sqrt{2x+6}$

## Step-by-step Solution

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###  Videos

$\frac{3x+6}{\sqrt{2x+6}}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(x\sqrt{2x+6}\right)$

Specify the solving method

1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\sqrt{2x+6}$

$\frac{d}{dx}\left(x\right)\sqrt{2x+6}+x\frac{d}{dx}\left(\sqrt{2x+6}\right)$

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

$\frac{d}{dx}\left(x\right)\sqrt{2x+6}+x\frac{d}{dx}\left(\sqrt{2x+6}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of x(2x+6)^1/2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{2x+6}. The derivative of the linear function is equal to 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}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

$\frac{3x+6}{\sqrt{2x+6}}$

##  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 d/dx(x(2x+6)^1/2) using the product ruleFind d/dx(x(2x+6)^1/2) using the quotient ruleFind d/dx(x(2x+6)^1/2) using logarithmic differentiationFind d/dx(x(2x+6)^1/2) using the definition

SnapXam A2

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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

### Main topic:

Differential Calculus

~ 0.11 s

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