# Definition of Derivative...4

Discussion in 'Calculus' started by nycmathguy, Jun 12, 2022.

1. ### nycmathguy

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Calculus
Section 2.8

With question 32 we end Section 2.8 and Chapter 2.

nycmathguy, Jun 12, 2022
2. ### MathLover1

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(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,

MathLover1, Jun 12, 2022
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3. ### nycmathguy

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nycmathguy, Jun 12, 2022
4. ### MathLover1

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correct

MathLover1, Jun 13, 2022
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5. ### nycmathguy

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Can you find the range using a graph for g(x) and
g '(x)?

nycmathguy, Jun 13, 2022
6. ### MathLover1

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yes -> The range is the set of possible output values, which are shown on the y-axis.

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

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

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

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

MathLover1, Jun 13, 2022
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7. ### nycmathguy

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How about finding the range for Definition of Derivatives...?

nycmathguy, Jun 13, 2022
8. ### MathLover1

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finding the range for Definition of Derivatives????? what that means

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

MathLover1, Jun 13, 2022
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