Final Answer
Step-by-step Solution
Specify the solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sqrt{x}$ and $g=e^{\left(x^2\right)}\left(x^2+1\right)^4$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\sqrt{x}\right)e^{\left(x^2\right)}\left(x^2+1\right)^4+\sqrt{x}\frac{d}{dx}\left(e^{\left(x^2\right)}\left(x^2+1\right)^4\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^1/2e^x^2(x^2+1)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{x} and g=e^{\left(x^2\right)}\left(x^2+1\right)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{\left(x^2\right)} and g=\left(x^2+1\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}.