Simplify the expression $\sqrt{\frac{e^{5x}\sin\left(e^{\tan\left(e^x\right)}\right)}{2}}$

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Final answer to the problem

$\frac{e^{\frac{5}{2}x}\sqrt{\sin\left(e^{\tan\left(e^x\right)}\right)}}{\sqrt{2}}$
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Step-by-step Solution

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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{\sqrt{e^{5x}\sin\left(e^{\tan\left(e^x\right)}\right)}}{\sqrt{2}}$

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$\frac{\sqrt{e^{5x}\sin\left(e^{\tan\left(e^x\right)}\right)}}{\sqrt{2}}$

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Learn how to solve problems step by step online. Simplify the expression ((e^(5x)sin(e^tan(e^x)))/2)^(1/2). The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt{e^{5x}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 5x and n equals \frac{1}{2}. Multiply the fraction and term in 5\cdot \left(\frac{1}{2}\right)x.

Final answer to the problem

$\frac{e^{\frac{5}{2}x}\sqrt{\sin\left(e^{\tan\left(e^x\right)}\right)}}{\sqrt{2}}$

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Function Plot

Plotting: $\frac{e^{\frac{5}{2}x}\sqrt{\sin\left(e^{\tan\left(e^x\right)}\right)}}{\sqrt{2}}$

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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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