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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(e^{3x^2}\right)\ln\left(x^2+1\right)+e^{3x^2}\frac{d}{dx}\left(\ln\left(x^2+1\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(e^(3x^2)ln(x^2+1)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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}. Applying the derivative of the exponential function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.