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(\left(\frac{x}{2}\right)^{\frac{2}{3}}\right)

Find the derivative of (x/2)^(2/3)

Answer

$\frac{\frac{6}{\sqrt[4]{3}}}{\sqrt[3]{x}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\left(\frac{x}{2}\right)^{\frac{2}{3}}\right)$
1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{2}{3}\left(\frac{x}{2}\right)^{-\frac{1}{3}}\cdot\frac{d}{dx}\left(\frac{x}{2}\right)$

Unlock this step-by-step solution!

Answer

$\frac{\frac{6}{\sqrt[4]{3}}}{\sqrt[3]{x}}$

Struggling with math?

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

$\frac{d}{dx}\left(\left(\frac{x}{2}\right)^{\frac{2}{3}}\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.29 seconds