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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\frac{d}{dx}\left(\frac{\sqrt{x\left(2x+3\right)^5}}{\sqrt{\left(7x-10\right)^{15}}}\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(((x(2x+3)^5)/((7x-10)^15))^1/2). The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. 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}}. Simplify \left(\sqrt{\left(7x-10\right)^{15}}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{15}{2} and n equals 2.