Monday

July 28, 2014

July 28, 2014

Posted by **ken** on Saturday, March 2, 2013 at 10:53pm.

thought i had this right, but again not finding the answer

which of the following gives the slope of the tangent line to the graph of y=2^(1-x) at x=2?

a)-1/2

b)1/2

c)-2

d)2

e)-(ln2)/2

so... it thought y=2^1-x)

then y'=(1-x)(2^(1-x-1))

at x=2

then y'=(1-2)(2^(1-2-1))

y'= -1(2^(-2))

y'= -1/4

any help figuring out where i went wrong would be greatly appreciated.

thank you

- calculus -
**Reiny**, Saturday, March 2, 2013 at 11:51pmy = 2^(1-x) is an exponential function, which is differentiated using natural logarithms

dy/dx = 2^(1-x) (-1) ( ln2)

so when x = 2,

dy/dx = -ln2(2^(1-2)

= -ln2 (1/2) = (-1/2)ln2 , looks like e

as soon as I had my derivative which contained ln2, I knew that the first 4 choices were not correct.

You found the derivative as if it was a polynomial function where the terms are such that the base is the variable, such as 3x^5

e.g.

compare 4^x with x^4

if y = x^4

dy/dx = 4x^3

but

if y = 4^x

dy/dx = ln4 (4^x)

- calculus -
**ken**, Sunday, March 3, 2013 at 12:37amThanks Reiny,really appreciate the extra explanation. get it now. thank you

**Related Questions**

English - Can you please check if these sentences are grammatically correct,...

Calculus - Hello...i just had a quick question...its probably something easy to ...

Chemistry-Repost for DrBob222 - A sample of C60O3 decomposes with an activation ...

Algebra :P... again - Hi! Sorry.. but 1 more question? Direction: Find the ...

English - I have a few doubts regarding the use of the present perfect. I really...

history - can some one check my work? i can where is it It's the one with the ...

Algebra - ello i need help factoring I haven't had factorin sense Algebra one ...

Algebra - Solve graphically. x-y=0 y=x² The reason I don't understand the ...

ict-SraJMcGin - Sorry i didn`t reply sooner ive only just looked at the post....

Math - I have a problem. A theater runs 2 movies The first movie is 40 minutes ...