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Find the implicit derivative $\frac{d}{dx}\left(y=\frac{3^{\left(1-7x\right)}+\arcsin\left(\sqrt{x}\right)}{\frac{log^1}{x}}\right)$

Step-by-step Solution

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Final Answer

$y^{\prime}=\frac{\left(-21\ln\left(3\right)3^{-7x}\sqrt{1-x}\sqrt{x}+\frac{1}{2}\right)\sqrt{x}+3\cdot 3^{-7x}\sqrt{1-x}+\sqrt{1-x}\arcsin\left(\sqrt{x}\right)}{\sqrt{1-x}log}$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(y=\frac{\left(3^{\left(1-7x\right)}+\arcsin\left(\sqrt{x}\right)\right)x}{log}\right)$

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$\frac{d}{dx}\left(y=\frac{\left(3^{\left(1-7x\right)}+\arcsin\left(\sqrt{x}\right)\right)x}{log}\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(y=(3^(1-7x)+arcsin(x^1/2))/((log^1)/x)). Simplify the derivative by applying the properties of logarithms. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of a function multiplied by a constant (\frac{1}{log}) is equal to the constant times the derivative of the function.

Final Answer

$y^{\prime}=\frac{\left(-21\ln\left(3\right)3^{-7x}\sqrt{1-x}\sqrt{x}+\frac{1}{2}\right)\sqrt{x}+3\cdot 3^{-7x}\sqrt{1-x}+\sqrt{1-x}\arcsin\left(\sqrt{x}\right)}{\sqrt{1-x}log}$

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Function Plot

Plotting: $y^{\prime}=\frac{\left(-21\ln\left(3\right)3^{-7x}\sqrt{1-x}\sqrt{x}+\frac{1}{2}\right)\sqrt{x}+3\cdot 3^{-7x}\sqrt{1-x}+\sqrt{1-x}\arcsin\left(\sqrt{x}\right)}{\sqrt{1-x}log}$

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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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