Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$\frac{1}{2}\left(\frac{\left(x+3\right)^9}{\left(4x-5\right)^{10}}\right)^{-\frac{1}{2}}\frac{d}{dx}\left(\frac{\left(x+3\right)^9}{\left(4x-5\right)^{10}}\right)$
Learn how to solve problems step by step online. Find the derivative of (((x+3)^9)/((4x-5)^10))^(1/2). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Since the exponent is negative, we can invert the fraction. 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(\left(4x-5\right)^{10}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 10 and n equals 2.
