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$\frac{d}{dx}\left(\frac{\sqrt[3]{\left(5x^7\right)^{8}}\sin\left(2x\right)}{\sqrt{2}+e^{3\cos\left(x\right)}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(((5x^7)^(8/3)sin(2x))/(2^1/2+e^(3cos(x)))). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.