👉 Try now NerdPal! Our new math app on iOS and Android

Find the derivative of $\left(4x^4-1\right)^{-\frac{1}{3}}$

Step-by-step Solution

Go!
Math 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

$\frac{-16x^{3}}{3\sqrt[3]{\left(4x^4-1\right)^{4}}}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

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

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

Learn how to solve differential calculus problems step by step online.

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

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve differential calculus problems step by step online. Find the derivative of (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. The derivative of the constant function (-1) is equal to zero. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function.

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 product ruleFind 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

Give us your feedback!

Function Plot

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

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:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

4. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account