Exercise
$\frac{d}{dx}\left(x^x\right)\left(3x-3\right)^3\cdot\left(4x^2+4\right)^4$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of x^x(3x-3)^3(4x^2+4)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\left(3x-3\right)^3\left(4x^2+4\right)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(3x-3\right)^3 and g=\left(4x^2+4\right)^4. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Find the derivative of x^x(3x-3)^3(4x^2+4)^4
Final answer to the exercise
$\left(\ln\left(x\right)+1\right)x^x\left(3x-3\right)^3\left(4x^2+4\right)^4+x^x\left(9\left(3x-3\right)^{2}\left(4x^2+4\right)^4+32\left(3x-3\right)^3\left(4x^2+4\right)^{3}x\right)$