Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1 and 2. f(x)=sqrt(x)

Question

Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1 and 2. f(x)=sqrt(x)

anonymous · Answer

still not clear what is meant by "rules" 
second one you should memorize 
$$f(x)=\sqrt{x},f'(x)=\frac{1}{2\sqrt{x}}$$

anonymous · Answer

(1.)
Rewrite the function as an exponent so that you can use the power rule, but you will also have to use the chain rule.
$$f(x)=1/(x+1) $$$$f(x)=(x-1)^{-1}$$
Chain Rule:
$$f \prime(x)= -(x-1)(1) = 1-x$$
(2.)
Write the square root function as x to the one half, again so that you can use the power rule.  Remember that you must subtract 1 from the exponent (rename as 2/2) to get -1/2.

$$ f(x)=\sqrt{x}$$
$$f(x)=x^{\frac{ 1 }{ 2 }}$$
$$f \prime(x)=\frac{ 1 }{ 2 } (x)^{\frac{ -1 }{ 2 }}$$
$$=\frac{ 1 }{ 2  \sqrt{x}}$$

anonymous · Answer

ooops

anonymous · Answer

try the first one again

anonymous · Answer

Snap, I don't feel like writing it out again, but it is $$-(x+1)^{-2}$$ which is equal to $$-\frac{ 1 }{( x+1)^{2} }$$
Subtract  1 ! Sorry about that.