Question

question find the derivative of y = x^5√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 $y = x^{5}\sqrt{x}=x^{5}x^{\frac{1}{2}}=x^{5 + \frac{1}{2}}=x^{\frac{10 + 1}{2}}=x^{\frac{11}{2}}$ using the rule $a^{m}\cdot a^{n}=a^{m + n}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = x^{n}$, then $y'=nx^{n - 1}$. For $y=x^{\frac{11}{2}}$, we have $y'=\frac{11}{2}x^{\frac{11}{2}-1}=\frac{11}{2}x^{\frac{11 - 2}{2}}=\frac{11}{2}x^{\frac{9}{2}}$.

Answer:

$\frac{11}{2}x^{\frac{9}{2}}$