What would the derivative of the area of a right triangle formula be?

A=(1/2)b*h

Question

What would the derivative of the area of a right triangle formula be?

A=(1/2)b*h

mathstudent55 · Answer

With respect ot which variable?

anonymous · Answer

With respect to time sorry!

mathstudent55 · Answer

Do both the base and height vary with respect to time?

anonymous · Answer

Yes, the problem is 

A 13 ft ladder is leaning against a house when its base begins to slide away. By the time the base is 3 ft from the house, the base is moving at the rate of 2 ft/sec. Answer the following: 

and I need to find:

At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?

But I think I messed up differentiating the area of the triangle!

mathstudent55 · Answer

y = uv
y' = uv' + vu'

anonymous · Answer

Yes. So is A'=(1/2)b'*h + (1/2)b*h' 

correct?

anonymous · Answer

Pretending the ( )' = d( )/dt

mathstudent55 · Answer

$A = \dfrac{1}{2}bh$

$A = \dfrac{1}{2}(bh)$

$\dfrac{dA}{dt} = \dfrac{1}{2}\dfrac{d}{dt}(bh)$

$\dfrac{dA}{dt} = \dfrac{1}{2} \left(b \dfrac{dh}{dt} + h \dfrac{b}{dt} \right)$

mathstudent55 · Answer

Yes, you are correct.

mathstudent55 · Answer

Sorry, last fraction above in last line should be db/dt

anonymous · Answer

Okay awesome thanks! :-)

mathstudent55 · Answer

yw