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Step-by-step Solution
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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{dx}\left(\sqrt{x}\right)e^{\left(x^2\right)}\left(x^2+1\right)^4+\sqrt{x}\left(\frac{d}{dx}\left(e^{\left(x^2\right)}\right)\left(x^2+1\right)^4+e^{\left(x^2\right)}\frac{d}{dx}\left(\left(x^2+1\right)^4\right)\right)$
Learn how to solve equations 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'. 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}. Applying the derivative of the exponential function.