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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
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$\frac{32\frac{d}{dx}\left(-e^x\cdot x^2-10e^x\cdot x-20e^x\right)e^{2x}-\left(-e^x\cdot x^2-10e^x\cdot x-20e^x\right)\frac{d}{dx}\left(32e^{2x}\right)}{\left(32e^{2x}\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx((-e^xx^2-10e^xx-20e^x)/(32e^(2x))). 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 power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(-e^x\cdot x^2-10e^x\cdot x-20e^x). Simplify the product -(-10e^x\cdot x-20e^x).