Question

differentiate the function, a(s) = -13/s⁴ a(s) = resources read it watch it submit answer 11. - / 4.54 points differentiate the function. y = √x(x - 14) y = resources read it watch it

Explanation:

Step1: Rewrite function with negative exponent

$A(s) = -13s^{-4}$

Step2: Apply power rule for differentiation

$A'(s) = -13 \cdot (-4)s^{-5} = 52s^{-5}$

Step3: Rewrite as positive exponent

$A'(s) = \frac{52}{s^5}$

Step4: Rewrite function with rational exponent

$y = x^{1/2}(x - 14) = x^{3/2} - 14x^{1/2}$

Step5: Differentiate term by term

$y' = \frac{3}{2}x^{1/2} - 14 \cdot \frac{1}{2}x^{-1/2} = \frac{3}{2}\sqrt{x} - \frac{7}{\sqrt{x}}$

Answer:

$\frac{52}{s^5}$
$\frac{3}{2}\sqrt{x} - \frac{7}{\sqrt{x}}$