Partial derivatives: S(w, h) = (15.63w^0.425) * (h^.0725)

[mooshupork34]

The function S(w, h) = (15.63w^0.425) * (h^.0725) gives the approximate surface area (in sq. inches) of a person h inches tall who weighs w pounds.

1) A boy grows taller while maintaining a weight of 130 pounds. At what rate is his surface area increasing when he's 5'4" tall?

2) Now at his full height of 5'9", he goes to the gym and bulks up. At what rate is his body surface increasing when he reaches 140 pounds?

 

[galactus]

Re: Partial derivatives problem

The function S(w, h) = (15.63w^0.425) * (h^.0725) gives the approximate surface area (in sq. inches) of a person h inches tall who weighs w pounds.

1) A boy grows taller while maintaining a weight of 130 pounds. At what rate is his surface area increasing when he's 5'4" tall?

\(\displaystyle \L\\S(w,h)=\frac{1563}{100}w^{\frac{17}{40}}h^{\frac{29}{400}}\)

They want dS/dh given w=130 and h=16/3. Differentiate S with respect to h.

That's because h is changing while w remains constant.

\(\displaystyle \L\\\frac{dS}{dh}=\frac{45327w^{\frac{17}{40}}}{40000h^{\frac{371}{400}}}\)

For the second one, differentiate with respect to w with h held fixed.

 

[mooshupork34]

Re: Partial derivatives problem

I was wondering...how did you get the numbers - meaning 45327, 40000, and 371/400?

 

[galactus]

I just converted your decimals to fractions and then differentiated.

I like fractions better than decimals. Looks better, I think. Just my thing.

 

[mooshupork34]

I just converted your decimals to fractions and then differentiated.

I like fractions better than decimals. Looks better, I think. Just my thing.

Ah, I see now! Thanks!

 

[mooshupork34]

I just converted your decimals to fractions and then differentiated.

I like fractions better than decimals. Looks better, I think. Just my thing.

Eh sorry, I'm a little confused about how to find the partial derivative with respect to w.