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When multiplying two powers that have the same base ($k+1$), you can add the exponents
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$\frac{d}{dk}\left(\frac{\left(k+1\right)^2+1}{2\left(2\left(k+1\right)+1\right)}\right)$
Learn how to solve one-variable linear equations problems step by step online. Find the derivative of ((k+1)(k+1)+1)/(2(2(k+1)+1)). When multiplying two powers that have the same base (k+1), you can add the exponents. 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 -(\left(k+1\right)^2+1).