Question

find the derivative of y = 2x - 7√x. be sure to include parentheses around the arguments of any logarithmic functions in your answer. provide your answer below: y = □

Explanation:

Step1: Rewrite the function

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

Step2: Apply the power - rule of differentiation

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

Step3: Combine the derivatives

$y^\prime=2-\frac{7}{2\sqrt{x}}$.

Answer:

$y^\prime = 2-\frac{7}{2\sqrt{x}}$