# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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^4*ln(x^4)+ln(x)^5) using the sum rule. The derivative of a sum of two 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}.

$9\left(4x^{3}\ln\left(x^4\right)+4x^{3}\right)+\frac{5\ln\left(x\right)^{4}}{x}$
$\frac{d}{dx}\left(9x^4\cdot\ln\left(x^4\right)+\ln\left(x\right)^5\right)$