Question

Find the gradient, picture below

Answer 1

Answer:

$\frac{dy}{dx} = \frac{13}{8}$

Step-by-step explanation:

$y = 2x + 6 {x}^{ - \frac{1}{2} } \\ \frac{dy}{dx} = 2 + 6( - \frac{1}{2}) {x}^{ - \frac{1}{2} - 1 } \\ \frac{dy}{dx} = 2 - 3 {x}^{ - \frac{3}{2} } \\ \frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {x}^{3} } }$

When x = 4,

$\frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {4}^{3} } } \\ = \frac{13}{8}$

Answer 2

Answer:

Hello,

Answer 13/8

Step-by-step explanation:

$y=2x+\dfrac{3}{\sqrt{x} } \\\\y'=2+6*\dfrac{-1}{2} x^{\frac{-3}{2} }\\\\y'=3-\frac{3}{\sqrt{x^3}} \\\\\\For x=4, \\\\y'(4)=2-\dfrac{3}{8} =\dfrac{13}{8}$