Final answer to the problem
$\left(\ln\left(x\right)+1\right)x^x\left(x+7\right)^4\left(7x+2\right)^3+x^x\left(4\left(x+7\right)^{3}\left(7x+2\right)^3+21\left(x+7\right)^4\left(7x+2\right)^{2}\right)$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(x^x(x+7)^4(7x+2)^3-y) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\left(x+7\right)^4\left(7x+2\right)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x+7\right)^4 and g=\left(7x+2\right)^3. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final answer to the problem
$\left(\ln\left(x\right)+1\right)x^x\left(x+7\right)^4\left(7x+2\right)^3+x^x\left(4\left(x+7\right)^{3}\left(7x+2\right)^3+21\left(x+7\right)^4\left(7x+2\right)^{2}\right)$
