Learn how to solve problems step by step online. Find the derivative of ln((x+1)^2(x-2)(x^2+3)). 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}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x+1\right)^2 and g=\left(x-2\right)\left(x^2+3\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x-2 and g=x^2+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}.

Find the derivative of ln((x+1)^2(x-2)(x^2+3))