Find the derivative of $\frac{\left(x^{- \frac{1}{5}}\sqrt{y^{3}}\right)^{10}}{\left(y^{- \frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$

Step-by-step Solution

Go!
Symbolic mode
Text mode
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

Final answer to the problem

$\frac{17y^{16}}{\sqrt[3]{x^{16}}}+\frac{-16y^{17}}{3\sqrt[3]{x^{19}}}$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Find the derivative
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Load more...
Can't find a method? Tell us so we can add it.
1

The power of a product is equal to the product of it's factors raised to the same power

$\frac{d}{dx}\left(\frac{\left(x^{-\frac{1}{5}}\right)^{10}\left(\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\right)^5\left(\sqrt[3]{x^{2}}\right)^5}\right)$

Learn how to solve problems step by step online.

$\frac{d}{dx}\left(\frac{\left(x^{-\frac{1}{5}}\right)^{10}\left(\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\right)^5\left(\sqrt[3]{x^{2}}\right)^5}\right)$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Find the derivative of ((x^(-1/5)y^(3/2))^10)/((y^(-2/5)x^(2/3))^5). The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(y^{-\frac{2}{5}}\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -\frac{2}{5} and n equals 5. Simplify \left(\sqrt[3]{x^{2}}\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{2}{3} and n equals 5. Simplify \left(x^{-\frac{1}{5}}\right)^{10} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -\frac{1}{5} and n equals 10.

Final answer to the problem

$\frac{17y^{16}}{\sqrt[3]{x^{16}}}+\frac{-16y^{17}}{3\sqrt[3]{x^{19}}}$

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

Help us improve with your feedback!

Function Plot

Plotting: $\frac{17y^{16}}{\sqrt[3]{x^{16}}}+\frac{-16y^{17}}{3\sqrt[3]{x^{19}}}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account