## Question

###### How do I find the derivative of #f(x)=x^3# from first principles?

How do I find the derivative of #f(x)=x^3# from first principles?

## Answers

First Principles#-># Difference Quotient

#f'(x)=lim_(h->0)(f(x+h)-f(x))/h#

#f(x)=x^3#

#f(x+h)=(x+h)^3#

#f'(x)=lim_(h->0)((x+h)^3-x^3)/h#

#f'(x)=lim_(h->0)((x+h)(x^2+2xh+h^2)-x^3)/h#

#f'(x)=lim_(h->0)(x^3+2x^2h+xh^2+x^2h+2xh^2+h^3-x^3)/h#

#f'(x)=lim_(h->0)(2x^2h+xh^2+x^2h+2xh^2+h^3)/h#

#f'(x)=lim_(h->0)(h*(2x^2+xh+x^2+2xh+h^2))/h#

#f'(x)=lim_(h->0)2x^2+xh+x^2+2xh+h^2#

#f'(x)=lim_(h->0)3x^2+xh+2xh+h^2#

#f'(x)=3x^2+x(0)+2x(0)+(0)^2#

#f'(x)=3x^2#

#### Similar Solved Questions

1 answers

##### What is the pH of a 0.1 molar sodium acetate(NaC2H302) solution? What is the concentration of...

What is the pH of a 0.1 molar sodium acetate(NaC2H302) solution? What is the concentration of each species present in the solution? (10 points) Ka(acetic acid) = 4.6 x 10-5 mole liter1 Kw = 1.0 x 10-14 mole2liter2...

1 answers

##### 1) Solve with reduction of order. y" + 7y' - 18y = ex + e2x

1) Solve with reduction of order. y" + 7y' - 18y = ex + e2x...

1 answers

##### I need help determining research from non-researchable questions. any help with this is appreciated. Read the...

i need help determining research from non-researchable questions. any help with this is appreciated. Read the following questions and determine which is/are researchable as written. Rewrite one non- researchable question as a researchable question. Give rationale for your responses and base answers ...

1 answers

##### Linear algebra Use the matrix P to determine if the matrices A and A' are similar....

linear algebra Use the matrix P to determine if the matrices A and A' are similar. P = 15 9 -20 -11 1 p-1 p-1AP = Are they similar? Yes, they are similar. No, they are not similar....

1 answers

##### Which of the following is the primary user of management accounting information regarding business units? Multiple...

Which of the following is the primary user of management accounting information regarding business units? Multiple Choice Industry and governmental organizations. Company management. Creditors Investors....

1 answers

##### Which of the following is the best description of the financial statement analysis framework? State the...

Which of the following is the best description of the financial statement analysis framework? State the objective and context, gather data, process the data, analyze and interpret the data, report the conclusions or recommendations, update the analysis. Gather data, analyze and interpret...

1 answers

##### T(T) - - - 1. The drawing at the right depicts a propeller with inertia J...

T(T) - - - 1. The drawing at the right depicts a propeller with inertia J about its centerline immersed in a fluid which acts as a damper, applying a torque in the opposite direction of the propeller's motion such that Ta=-co. The propeller is subject to a non-harmonic, periodic torque T(t) from...

1 answers

##### Choose the most direct pathway for an oxygen molecule, from entering the blood at the lungs,...

Choose the most direct pathway for an oxygen molecule, from entering the blood at the lungs, until it is utilized in cellular respiration by a hepatocyte: (Heart & lungs) hepatic vein central vein sinusoid rightarrow hepatocyte (Heart & lungs) rightarrow hepatic artery portal venule sinusoid...

1 answers

##### Question 2 of 3 (1 point) View problem in a pop-up 11.1 Section Exercise 8 (calc)...

Question 2 of 3 (1 point) View problem in a pop-up 11.1 Section Exercise 8 (calc) Action % of time 70.8 8.2 9.0 12.0 On time National Aviation System delay Aircraft arriving late Other (because of weather and other conditions) Download data Source: www.transtats.bts.gov Records of 200 flights for a ...

1 answers

##### Please help with a detailed, fully explained answer for Question 2. thank you Read the case...

please help with a detailed, fully explained answer for Question 2. thank you Read the case study below and answer the questions. SHORT RUN STABILIZATION AND LONG RUN COMPETITIVENESS: THE LAVITAN CASE Growth of a young country Latvia - a small, young country on the east coast of the Baltic Sea -has ...

1 answers

##### The drawing shows a wire composed of three segments, AB, BC, and CD. There is a...

The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current of I = 2.2 A in the wire. There is also a magnetic field B (magnitude = 0.29 T) that is the same everywhere and points in the direction of +z axis. The lengths of the wire segments are LAB = 1.3 m, LBC = 0.5 m, a...

1 answers

##### Nt Score: 250/1100 Resources LX Give Up? Feedback of 11 A projectile is fired at o...

nt Score: 250/1100 Resources LX Give Up? Feedback of 11 A projectile is fired at o 342.0 m/s at an angle of θ 67.5, with respect to the horizontal. Assume that air friction will shorten the range by 30.1%. How far will the projectile travel in the horizontal direction, R? distance traveled: 14...

1 answers

##### Half a bottle of scotch whiskey is consumed and returned to the cabinet uncorked. Initially the...

Half a bottle of scotch whiskey is consumed and returned to the cabinet uncorked. Initially the scotch contained 400 grams of ethanol. The unsealed bottle loses ethanol at rate of 0.5grams per day. After sitting in the cabinet over the summer (90 days) with the cork removed, how much alcohol remains...