Product rule (f g)' = f ' g + f g', Mathematics

Assignment Help:

Product Rule: (f g)′ = f ′ g + f g′

As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved by using Logarithmic Differentiation. We will demonstrate both proofs now.

Proof

It is a much faster proof but does assume that you have read and understood Logarithmic Differentiation and the Implicit Differentiation sections. If you have not so this proof will not make much sense to you.

Firstly write call the product y and get the log of both sides and utilize a property of logarithms upon the right side.

y = f(x)  g(x)    

ln(y) = ln (f(x)  g(x)) = ln f(x) + ln g(x)

Subsequently, we take the derivative of both sides and then solve for y′.

y'/y = (f'(x)/f(x)) + (g'(x)/g(x))                         =>                    y' = y (f'(x)/f(x)) + (g'(x)/g(x))

At last, all we require to do is plug into for y and after that multiply this with the parenthesis and we find the Product Rule.

y = f(x) g(x) (f'(x)/f(x)) + (g'(x)/g(x))  =>                    (fg)' = g(x) f'(x) + f(x) g'(x)


Related Discussions:- Product rule (f g)' = f ' g + f g'

Find the perimeter and the area of the shaded portion, The given figure con...

The given figure consists of four small semicircles and two big semicircles.  If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find

Solve -10 cos(3t )= 7 on [-2, Solve -10 cos(3t )= 7 on [-2,5]. Solution...

Solve -10 cos(3t )= 7 on [-2,5]. Solution Let's first get the inverse cosine portion of this problem taken care of. cos(3 t )= -  7/10            ⇒     3t = cos -1 ( - 7

Sampling distribution p-hat, Caterer verifies that 87% of people who sample...

Caterer verifies that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If

Math probles, Belleville lake was originally blue because it only had 11 al...

Belleville lake was originally blue because it only had 11 algae plants. then towns and farms cropped up by the lake .this cause 446 more algae plants to grow which turned the lake

Debate over answer to an equation..., The math equation is written exactly ...

The math equation is written exactly this way: 0+50x1-60-60x0+10=??? The answer I get is 10 and others say 0 0+50=50 50x1=50 50-60=-10 -10-60=-70 -70x0=0 0+10=10

In an election contested between a and b determine vote, In an election con...

In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twi

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd