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$\frac{d}{dx}\left(\left(x^2-\frac{3}{2}\right)\sqrt{5x+3}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (x^2+-3/2)(5x+3)^1/2. Simplifying. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2-\frac{3}{2} and g=\sqrt{5x+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.