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Find the derivative using the product rule $\frac{d}{dx}\left(\left(4x^4-1\right)^{-\frac{1}{3}}\right)$

Step-by-step Solution

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Final Answer

$\frac{-16x^{3}}{3\sqrt[3]{\left(4x^4-1\right)^{4}}}$
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Step-by-step Solution

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

$-\frac{1}{3}\left(4x^4-1\right)^{-\frac{4}{3}}\frac{d}{dx}\left(4x^4-1\right)$

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$-\frac{1}{3}\left(4x^4-1\right)^{-\frac{4}{3}}\frac{d}{dx}\left(4x^4-1\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx((4x^4-1)^(-1/3)). 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 a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=4 and g=x^4. The derivative of the constant function (4) is equal to zero.

Final Answer

$\frac{-16x^{3}}{3\sqrt[3]{\left(4x^4-1\right)^{4}}}$

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 derivative of (4x^4-1)^(-0.3333) using the quotient ruleFind derivative of (4x^4-1)^(-0.3333) using logarithmic differentiationFind derivative of (4x^4-1)^(-0.3333) using the definition

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Plotting: $\frac{-16x^{3}}{3\sqrt[3]{\left(4x^4-1\right)^{4}}}$

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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:

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 $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

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