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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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Final Answer

$\left(\frac{20x^{4}+12}{x^5+3x}+\tan\left(x\right)\right)\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$
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Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

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.

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

Unlock this full step-by-step solution!

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. Derive both sides of the equality with respect to x. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.

Final Answer

$\left(\frac{20x^{4}+12}{x^5+3x}+\tan\left(x\right)\right)\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$
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Got another answer? Verify it!

Go!
1
2
3
4
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

Tips on how to improve your answer:

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

Related Formulas:

6. See formulas

Time to solve it:

~ 0.2 s