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# Find the derivative $\frac{d}{dx}\left(9x^4\ln\left(x^4\right)+\ln\left(x\right)^5\right)$ using the sum rule

## Step-by-step Solution

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###  Videos

$\frac{36x^{4}\ln\left(x^4\right)+36x^{4}+5\ln\left(x\right)^{4}}{x}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)+\ln\left(x\right)^5\right)$

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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(9x^4ln(x^4)+ln(x)^5) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (9) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^4 and g=\ln\left(x^4\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

$\frac{36x^{4}\ln\left(x^4\right)+36x^{4}+5\ln\left(x\right)^{4}}{x}$

##  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 (9x^4+lnx^5) using the product ruleFind derivative of (9x^4+lnx^5) using the quotient ruleFind derivative of (9x^4+lnx^5) using logarithmic differentiation

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a
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x
y
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(◻)
+
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◻/◻
/
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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:

Sum Rule of Differentiation

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