Help w/ deriv. of f(x+2), dy/dx of (3x)/(x^2+1), etc.

[bobithjones]

Hey guys, having some trouble with math homework

1) what is the derivative of f(x+2) **function is unknown

2) dy/dx of (3x)/(x^2+1)

3) find (d^2x)/(dx^2) in terms of x and y for 1-xy= x-y

4) a player is runnign from 1st to 2nd base (90 Feet Apart) at a speed of 28 ft/sec. find the rate at which the distance from home plate is changing when the plyer is 30 feet away from Second base

thank you so much
____________________
Edited by stapel -- Reason for edit: Numbering questions.

 

[galactus]

Re: Help with derivatives

For the first one, think chain rule.

For the second one, it's just a matter of the quotient rule.

For the third, implicit differentiation...twice. Write as \(\displaystyle 1-xy-x+y=0\)

Differentiate implicitly,\(\displaystyle -(xy'+y)-1+y'=0\). Now, solve for \(\displaystyle y'=\frac{y+1}{1-x}\)

Do it again now to find y''. Don't forget to sub in y'.


Use Pythagoras. Afterall, a baseball diamond is essentially a tilted square.

The distance from Home plate to 1st base is also 90 feet. You need a point, P, between first and second.

\(\displaystyle D^{2}=x^{2}+y^{2}\)

Let x=distance from first to the player. Let y=distance from homeplate to first.

Therefore, the distance from home to the player is \(\displaystyle D=\sqrt{60^{2}+90^{2}}=30\sqrt{13}\approx{108.17}\)

Differentiate our distance formula: \(\displaystyle D\frac{dD}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}\)

Now, fill in your knowns and solve for dD/dt. Remember dy/dt does not change.

 

[bobithjones]

Re: Help with derivatives

galactus, thank you so much