Find the derivative using the quotient rule $\frac{3}{4}x\cos\left(x\right)\sin\left(x\right)\cos\left(x\right)-\sqrt{24\cdot \left(\frac{3}{4}\right)x\sin\left(x\right)}+13=x-\frac{3}{4}\sin\left(x\right)^3$

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$1+\frac{d}{dx}\left(-\frac{3}{4}\sin\left(x\right)^3\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule cos(x)x3/4sin(x)cos(x)-(243/4sin(x)x)^(1/2)+13=x-3/4sin(x)^3. 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply the fraction and term in 3\left(-\frac{3}{4}\right)\sin\left(x\right)^{2}\frac{d}{dx}\left(\sin\left(x\right)\right).