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Find the derivative of $\sqrt{x}\ln\left(x\right)$

Step-by-step Solution

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sinh
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asinh
acosh
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$\frac{\ln\left(x\right)+2}{2\sqrt{x}}$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\sqrt{x}\ln\left(x\right)\right)$

Specify the solving method

1

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

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

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

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

Learn how to solve differential calculus problems step by step online. Find the derivative of x^1/2ln(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{x} and g=\ln\left(x\right). 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 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 the linear function is equal to 1.

$\frac{\ln\left(x\right)+2}{2\sqrt{x}}$
SnapXam A2

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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

$\frac{d}{dx}\left(\sqrt{x}\ln\left(x\right)\right)$