differentiate (2 Viewers)

[EinstenICEBERG]

y = 5^x Hint: 5= e^ln5

i dont get the hint .... and i dont know how to differentiate it

 

[SpiralFlex]

Notice and are each others' inverse function

In general,




The hint is quite misleading (in a sense)





Using your exponential differentiation,

 

[Carrotsticks]

 

[EinstenICEBERG]

can u tell me how u get e^xln 5 = 5^x

in the differentiate part

 

[Carrotsticks]

Oh and as a general rule:



For some a > 0

 

[EinstenICEBERG]

where u get that log law... i cant find it in my text book..

 

[Carrotsticks]

can u tell me how u get e^xln 5 = 5^x

in the differentiate part

The e and the ln kinda 'cancel' each other out, leaving 5^x.

 

[EinstenICEBERG]

ok i will try to figure it out thanks carrot and spiral

 

[SpiralFlex]

can u tell me how u get e^xln 5 = 5^x

in the differentiate part

Where a is a constant.



As we showed before.

 

[EinstenICEBERG]

ye its not in my text book that why they gave me a hint ... WOW

 

[Carrotsticks]

where u get that log law... i cant find it in my text book..

Provided that a > 0

 

[barbernatorr]

the long way around the differential,

y = a^x
ln(y) = ln(a^x)
= x ln(a)
therefore,
x = ln(y) / ln(a)
dx/dy = 1/(y ln(a))
dy/dx = y ln(a)

therefore,
dy/dx = a^x (ln(a))

sorry for no latex, but yeh

 

[Carrotsticks]

the long way around the differential,

y = a^x
ln(y) = ln(a^x)
= x ln(a)
therefore,
x = ln(y) / ln(a)
dx/dy = 1/(y ln(a))
dy/dx = y ln(a)

therefore,
dy/dx = a^x (ln(a))

sorry for no latex, but yeh

I actually prefer this way because it is a useful technique for many other differentiating questions, whereas the method we used here does not always work.

 

[deswa1]

Also for 4U students who can implicitly differentiate, this also comes in handy for a few types of questions:
<img src="http://latex.codecogs.com/gif.latex?y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" title="y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" />

 

[barbernatorr]

Also for 4U students who can implicitly differentiate, this also comes in handy for a few types of questions:
<img src="http://latex.codecogs.com/gif.latex?y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" title="y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" />

this ^. Implicit differentiation should be taught to 3 unit students as well IMO

 

[Timske]

I remember doing implicit diff in a 3u booklet

 

[SpiralFlex]

Some teachers do implicit in 2-3U.

 

[SpiralFlex]

ALSO @TIMSKE YOU GOT PHYSICS TOMORROW. WHY ARE YOU ON?!

 

[barbernatorr]

The greatest thread ever

teach me to be like you

 

[Timske]

ALSO @TIMSKE YOU GOT PHYSICS TOMORROW. WHY ARE YOU ON?!

Im all set...NOT>