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Find the derivative of $14\sqrt[4]{a^5b^2}c^4-7a\sqrt[4]{cab^2}$

Step-by-step Solution

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Final Answer

$\frac{35c^4\sqrt[4]{a}\sqrt{b}}{2}+\frac{7c^4\sqrt[4]{a^{5}}}{\sqrt{b}}-\frac{35}{4}\sqrt[4]{a}\sqrt[4]{c}\sqrt{b}+\frac{-7\sqrt[4]{a^{5}}\sqrt[4]{c}}{2\sqrt{b}}$
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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

$\frac{d}{db}\left(14\sqrt[4]{a^5b^2}c^4\right)+\frac{d}{db}\left(-7a\sqrt[4]{cab^2}\right)$

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$\frac{d}{db}\left(14\sqrt[4]{a^5b^2}c^4\right)+\frac{d}{db}\left(-7a\sqrt[4]{cab^2}\right)$

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Learn how to solve differential equations problems step by step online. Find the derivative of 14(a^5b^2)^1/4c^4-7a(cab^2)^1/4. 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 is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power of a product is equal to the product of it's factors raised to the same power.

Final Answer

$\frac{35c^4\sqrt[4]{a}\sqrt{b}}{2}+\frac{7c^4\sqrt[4]{a^{5}}}{\sqrt{b}}-\frac{35}{4}\sqrt[4]{a}\sqrt[4]{c}\sqrt{b}+\frac{-7\sqrt[4]{a^{5}}\sqrt[4]{c}}{2\sqrt{b}}$

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 (14a^5b^2^0.25+-7a) using the product ruleFind derivative of (14a^5b^2^0.25+-7a) using the quotient ruleFind derivative of (14a^5b^2^0.25+-7a) using logarithmic differentiationFind derivative of (14a^5b^2^0.25+-7a) using the definition

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Function Plot

Plotting: $\frac{35c^4\sqrt[4]{a}\sqrt{b}}{2}+\frac{7c^4\sqrt[4]{a^{5}}}{\sqrt{b}}-\frac{35}{4}\sqrt[4]{a}\sqrt[4]{c}\sqrt{b}+\frac{-7\sqrt[4]{a^{5}}\sqrt[4]{c}}{2\sqrt{b}}$

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7
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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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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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