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Find the derivative of $\frac{64a^3+343}{4a+7}$ using the definition

Step-by-step Solution

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Final Answer

$-28+32a$
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Step-by-step Solution

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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$

$derivdef\left(\frac{\left(4a+7\right)\left(16a^{2}-28a+49\right)}{4a+7}\right)$

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$derivdef\left(\frac{\left(4a+7\right)\left(16a^{2}-28a+49\right)}{4a+7}\right)$

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Learn how to solve problems step by step online. Find the derivative of (64a^3+343)/(4a+7) using the definition. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify the fraction \frac{\left(4a+7\right)\left(16a^{2}-28a+49\right)}{4a+7} by 4a+7. Find the derivative of 16a^{2}-28a+49 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 16a^{2}-28a+49. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -28 by each term of the polynomial \left(a+h\right).

Final Answer

$-28+32a$

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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 derivdef((64a^3+343)/(4a+7)) using the product ruleFind derivdef((64a^3+343)/(4a+7)) using the quotient ruleFind derivdef((64a^3+343)/(4a+7)) using logarithmic differentiation

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Function Plot

Plotting: $-28+32a$

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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
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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