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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}\right)$

Step-by-step Solution

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$\left(\frac{4\left(5x^{4}+3\right)}{x^5+3x}+\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$
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 Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}\right)$

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To derive the function $\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$, use the method of logarithmic differentiation. First, assign the function to $y$, then take the natural logarithm of both sides of the equation

$y=\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$

Learn how to solve logarithmic differentiation problems step by step online.

$y=\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$

Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(((x^5+3x)^4)/(cos(x)). To derive the function \frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Apply logarithm properties to both sides of the equality. Derive both sides of the equality with respect to x.

$\left(\frac{4\left(5x^{4}+3\right)}{x^5+3x}+\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$

 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 ((x^5+3x)^4)/cosx using the product ruleFind derivative of ((x^5+3x)^4)/cosx using the quotient ruleFind derivative of ((x^5+3x)^4)/cosx using the definition

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7
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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

Main topic:

Logarithmic Differentiation

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