Definition of Derivative...4

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Calculus
Section 2.8

Screenshot_20220610-183308_Samsung Notes.jpg


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With question 32 we end Section 2.8 and Chapter 2.
 
(d/dx)(1/(1 + sqrt(x))). ......aply exponent rule 1/a=a^-1

=(d/dx)((1 + sqrt(x))^-1)..............apply chain rule

=-1/(1 + sqrt(x))^2*(d/dx)((1 + sqrt(x))............(d/dx)((1 + sqrt(x))=1/(2sqrt(x))

=-1/(1 + sqrt(x))^2*1/(2sqrt(x)).......simplify

=-1/((1 + sqrt(x))^2*2sqrt(x))

so,
upload_2022-6-12_16-33-7.gif
 
yes -> The range is the set of possible output values, which are shown on the y-axis.

f(x)=1/(1+sqrt(x))

MSP20611hee23ice8h24f6a00002h14b05c6826791h



range: { y element R : 0<y<=1}

upload_2022-6-12_18-22-24.gif



f'(x)=-1/((1 + sqrt(x))^2*2sqrt(x))

MSP58419agc692dff2fgeh00003i799f988dei7eic


range:{ y element R : y<0} (all negative real numbers)

upload_2022-6-12_18-27-6.gif
 
finding the range for Definition of Derivatives????? what that means

you can find the derivative of the function using the definition of derivative
 
finding the range for Definition of Derivatives????? what that means

you can find the derivative of the function using the definition of derivative

I meant to ask:

Can you please find the range for 26 and 28 located at the link provided?
 

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