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Find the derivative using the product rule $\frac{d}{da}\left(\frac{v^2r}{a\left(\left(r+b^2r^1\right)^2+\left(x+b^2x^1\right)^2\right)}\right)$

Step-by-step Solution

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Final Answer

$\frac{\left(-\left(r+b^2r\right)^2-\left(x+b^2x\right)^2\right)v^2r}{a^2\left(\left(r+b^2r\right)^2+\left(x+b^2x\right)^2\right)^2}$
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Step-by-step Solution

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$\frac{d}{da}\left(\frac{v^2r}{a\left(\left(r+b^2r\right)^2+\left(x+b^2x^1\right)^2\right)}\right)$

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$\frac{d}{da}\left(\frac{v^2r}{a\left(\left(r+b^2r\right)^2+\left(x+b^2x^1\right)^2\right)}\right)$

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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/da((v^2r)/(a((r+b^2r^1)^2+(x+b^2x^1)^2))). Simplifying. Any expression to the power of 1 is equal to that same expression. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=v^2 and g=r.

Final Answer

$\frac{\left(-\left(r+b^2r\right)^2-\left(x+b^2x\right)^2\right)v^2r}{a^2\left(\left(r+b^2r\right)^2+\left(x+b^2x\right)^2\right)^2}$

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Find the derivativeFind derivative of v^2r/a((r+b^2r^1)^2+(x+b^2x^1)^2) using the quotient ruleFind derivative of v^2r/a((r+b^2r^1)^2+(x+b^2x^1)^2) using logarithmic differentiationFind derivative of v^2r/a((r+b^2r^1)^2+(x+b^2x^1)^2) using the definition

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Function Plot

Plotting: $\frac{\left(-\left(r+b^2r\right)^2-\left(x+b^2x\right)^2\right)v^2r}{a^2\left(\left(r+b^2r\right)^2+\left(x+b^2x\right)^2\right)^2}$

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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

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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

4. See formulas

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