Question

question find the derivative of (y = 2x-\frac{7}{sqrt{x}}). be sure to include parentheses around the arguments of any logarithmic functions in your answer. sorry, thats incorrect. try again? (y = 2x-\frac{7}{sqrt{x}})

Explanation:

Step1: Rewrite the function

Rewrite $y = 2x-\frac{7}{\sqrt{x}}$ as $y=2x - 7x^{-\frac{1}{2}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the first term $2x$ where $a = 2$ and $n = 1$, the derivative is $2\times1\times x^{1 - 1}=2$. For the second term $-7x^{-\frac{1}{2}}$, where $a=-7$ and $n =-\frac{1}{2}$, the derivative is $-7\times(-\frac{1}{2})x^{-\frac{1}{2}-1}=\frac{7}{2}x^{-\frac{3}{2}}$.

Step3: Combine the derivatives

$y^\prime=2+\frac{7}{2x^{\frac{3}{2}}}$.

Answer:

$y^\prime=2+\frac{7}{2x^{\frac{3}{2}}}$