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Find the derivative using the product rule $\frac{m^3n\sqrt{x}}{\sqrt[5]{2^4m^7n^6x}}$

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Solution

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Final answer to the problem

$\frac{\sqrt[5]{m^{8}}\sqrt[10]{x^{3}}}{\sqrt[5]{16}\sqrt[5]{n}}$
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Step-by-step Solution

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$\frac{m^3n\sqrt{x}}{\sqrt[5]{16m^7n^6x}}$

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$\frac{m^3n\sqrt{x}}{\sqrt[5]{16m^7n^6x}}$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (m^3nx^1/2)/((2^4m^7n^6x)^1/5). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. .

Final answer to the problem

$\frac{\sqrt[5]{m^{8}}\sqrt[10]{x^{3}}}{\sqrt[5]{16}\sqrt[5]{n}}$

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

Find the derivativeFind m^3n/(2^4m^7^0.2) using the quotient ruleFind m^3n/(2^4m^7^0.2) using logarithmic differentiationFind m^3n/(2^4m^7^0.2) using the definition

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Function Plot

Plotting: $\frac{\sqrt[5]{m^{8}}\sqrt[10]{x^{3}}}{\sqrt[5]{16}\sqrt[5]{n}}$

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5
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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
D□x
∫
∫◻
|◻|
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

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

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