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The power of a product is equal to the product of it's factors raised to the same power
Learn how to solve quotient rule of differentiation problems step by step online.
$\frac{d}{dx}\left(\frac{\sqrt{\ln\left(x\right)}\sqrt{\sin\left(x\right)^{5}}}{\sec\left(x\right)^2}\right)$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(((sin(x)^5ln(x))^1/2)/(sec(x)^2)). 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(\sec\left(x\right)^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{\sin\left(x\right)^{5}} and g=\sqrt{\ln\left(x\right)}.