Hi

Can someone tell me if my answers are correct for the following questions:

1) Find the slope of the graph$\displaystyle y=2x^3 + 4\sqrt{x}$ at x = 2

$\displaystyle \frac{dy}{dx} = 6x^2 + 2x^{\frac{-1}{2}}$

when x = 2

$\displaystyle \frac{dy}{dx} = 24 + \frac{1}{2\sqrt{2}}$

so the slope at x=2 is 24.3536

2)Evaluate the derivative: $\displaystyle \frac{d}{dx}[\frac{x^2-5x+1}{x^2+2x-1}]$

$\displaystyle = \frac{2x-5}{2x+2}$

3) Find $\displaystyle \frac{dx}{dt}$ when $\displaystyle x = (5-3t)^{4t}$

$\displaystyle \frac{dx}{dt} = 4t(5-3t)^{4t}$

$\displaystyle \frac{dx}{dt} = -12t(5-3t)^{4t-1}$

P.S