Question

question find the derivative of y = 6x - 6√x. provide your answer below. y = □

Explanation:

Step1: Rewrite the function

Rewrite $y = 6x - 6\sqrt{x}=6x-6x^{\frac{1}{2}}$.

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 $6x$ where $a = 6$ and $n = 1$, its derivative is $6\times1\times x^{1 - 1}=6$. For the second term $-6x^{\frac{1}{2}}$ where $a=-6$ and $n = \frac{1}{2}$, its derivative is $-6\times\frac{1}{2}x^{\frac{1}{2}-1}=-3x^{-\frac{1}{2}}$.

Step3: Combine the derivatives

$y^\prime=6 - 3x^{-\frac{1}{2}}$.

Answer:

$y^\prime=6-\frac{3}{\sqrt{x}}$