Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(\sqrt{x}\ln\left(x\right)\right)$

Go!
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Step-by-step Solution

Problem to solve:

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

Solving method

Learn how to solve integrals of rational functions problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve integrals of rational functions problems step by step online. Find the derivative using the product rule (d/dx)(x^0.5ln(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.

Final Answer

$\frac{\frac{1}{2}\ln\left(x\right)+1}{\sqrt{x}}$
SnapXam A2
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0
a
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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

Tips on how to improve your answer:

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

Time to solve it:

~ 0.62 s