Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Find the derivative using the product rule (d/dx)(ln(x^2+2)^3(1-x^3)^4)

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$\ln\left(x^2+2\right)^{2}x\left(1-x^3\right)^4\frac{6}{x^2+2}-12\ln\left(x^2+2\right)^3\left(1-x^3\right)^{3}x^{2}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(ln\left(x^2+2\right)^3\left(1-x^3\right)^4\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\ln\left(x^2+2\right)^3$ and $g=\left(1-x^3\right)^4$

$\left(1-x^3\right)^4\frac{d}{dx}\left(\ln\left(x^2+2\right)^3\right)+\ln\left(x^2+2\right)^3\frac{d}{dx}\left(\left(1-x^3\right)^4\right)$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$3\ln\left(x^2+2\right)^{2}\left(1-x^3\right)^4\frac{d}{dx}\left(\ln\left(x^2+2\right)\right)+4\ln\left(x^2+2\right)^3\left(1-x^3\right)^{3}\cdot\frac{d}{dx}\left(1-x^3\right)$

Unlock this step-by-step solution!

Answer

$\ln\left(x^2+2\right)^{2}x\left(1-x^3\right)^4\frac{6}{x^2+2}-12\ln\left(x^2+2\right)^3\left(1-x^3\right)^{3}x^{2}$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

$\frac{d}{dx}\left(ln\left(x^2+2\right)^3\left(1-x^3\right)^4\right)$

Main topic:

Differential calculus

Used formulas:

6. See formulas

Time to solve it:

~ 0.38 seconds