Final Answer
Step-by-step Solution
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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 $g=\left(1-x^3\right)^4$
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$\frac{d}{dx}\left(\ln\left(x^2+2\right)^3\right)\left(1-x^3\right)^4+\ln\left(x^2+2\right)^3\frac{d}{dx}\left(\left(1-x^3\right)^4\right)$
Learn how to solve differential equations problems step by step online. Find the derivative of ln(x^2+2)^3(1-x^3)^4. 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. 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}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.