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 $f=\sqrt{x}$ and $g=7\sqrt{x}-4x^3$
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$\frac{d}{dx}\left(\sqrt{x}\right)\left(7\sqrt{x}-4x^3\right)+\sqrt{x}\frac{d}{dx}\left(7\sqrt{x}-4x^3\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx(x^1/2(7x^1/2-4x^3)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{x} and g=7\sqrt{x}-4x^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}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.