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Find the derivative $\frac{d}{dx}\left(12x^5-4x^{-4}+\frac{3}{2\sqrt[3]{x^{2}}}\right)$ using the sum rule

Step-by-step Solution

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Final Answer

$\frac{60x^{9}+16-\sqrt[3]{x^{10}}}{x^{5}}$
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Step-by-step Solution

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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(12x^5\right)+\frac{d}{dx}\left(-4x^{-4}\right)+\frac{d}{dx}\left(\frac{3}{2\sqrt[3]{x^{2}}}\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(12x^5\right)+\frac{d}{dx}\left(-4x^{-4}\right)+\frac{d}{dx}\left(\frac{3}{2\sqrt[3]{x^{2}}}\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(12x^5-4x^(-4)3/(2x^2/3)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (12) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-4) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final Answer

$\frac{60x^{9}+16-\sqrt[3]{x^{10}}}{x^{5}}$

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 (12x^5+-4x^(-4)) using the product ruleFind derivative of (12x^5+-4x^(-4)) using the quotient ruleFind derivative of (12x^5+-4x^(-4)) using logarithmic differentiationFind derivative of (12x^5+-4x^(-4)) using the definition

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Plotting: $\frac{60x^{9}+16-\sqrt[3]{x^{10}}}{x^{5}}$

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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

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