👉 Try now NerdPal! Our new math app on iOS and Android

Find the derivative of $f\ln\left(\frac{x^5}{3x^2+6x+2}\right)$

Step-by-step Solution

Go!
Symbolic mode
Text mode
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

Final answer to the problem

$\ln\left(\frac{x^5}{3x^2+6x+2}\right)+\frac{\left(5x^{4}\left(3x^2+6x+2\right)+\left(-6x-6\right)x^5\right)f}{x^5\left(3x^2+6x+2\right)}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=

$\frac{d}{df}\left(f\right)\ln\left(\frac{x^5}{3x^2+6x+2}\right)+f\frac{d}{df}\left(\ln\left(\frac{x^5}{3x^2+6x+2}\right)\right)$

Learn how to solve definite integrals problems step by step online.

$\frac{d}{df}\left(f\right)\ln\left(\frac{x^5}{3x^2+6x+2}\right)+f\frac{d}{df}\left(\ln\left(\frac{x^5}{3x^2+6x+2}\right)\right)$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve definite integrals problems step by step online. Find the derivative of fln((x^5)/(3x^2+6x+2)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Divide fractions \frac{1}{\frac{x^5}{3x^2+6x+2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final answer to the problem

$\ln\left(\frac{x^5}{3x^2+6x+2}\right)+\frac{\left(5x^{4}\left(3x^2+6x+2\right)+\left(-6x-6\right)x^5\right)f}{x^5\left(3x^2+6x+2\right)}$

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 fln((x^5)/(3x^2+6x)) using the product ruleFind derivative of fln((x^5)/(3x^2+6x)) using the quotient ruleFind derivative of fln((x^5)/(3x^2+6x)) using logarithmic differentiationFind derivative of fln((x^5)/(3x^2+6x)) using the definition

Give us your feedback!

Function Plot

Plotting: $\ln\left(\frac{x^5}{3x^2+6x+2}\right)+\frac{\left(5x^{4}\left(3x^2+6x+2\right)+\left(-6x-6\right)x^5\right)f}{x^5\left(3x^2+6x+2\right)}$

SnapXam A2
Answer Assistant

beta
Got a different 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

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account