Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
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)

Find the derivative of x^0.5ln(x)

Answer

$\frac{1+\frac{1}{2}\ln\left(x\right)}{\sqrt{x}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\sqrt{x}\ln\left(x\right)\right)$
1

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

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

Unlock this step-by-step solution!

Answer

$\frac{1+\frac{1}{2}\ln\left(x\right)}{\sqrt{x}}$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.69 seconds