Help with Differentiation

[MoShow]

I am having trouble differentiating the following function with respect to x.

h(x)=(1-4x)^2

Ive looked online for help and I keep seeing (chain rule). My question is, is there another name for the chain rule? or is there another method to differentiate this function? Ive searched my book and I cant find anything even similar to the chain rule. Ive also looked for similar examples in the book for differentiation and have come up with nothing.

any help will be greatly appreciated.

 

[Ishuda]

I am having trouble differentiating the following function with respect to x.

h(x)=(1-4x)^2

Ive looked online for help and I keep seeing (chain rule). My question is, is there another name for the chain rule? or is there another method to differentiate this function? Ive searched my book and I cant find anything even similar to the chain rule. Ive also looked for similar examples in the book for differentiation and have come up with nothing.

any help will be greatly appreciated.

See if there is something under differentiating compositions of functions.

The chain rule [differentiating compositions of functions] says that
d(f(g(x))/dx = d(f(x))/dx|_x=g(x) d(g(x))/dx
Note that this can continue indefinitely, i.e.
d(f(g(h(x)))/dx = d(f(x))/dx|_x=g(h(x)) d(g(x))/dx|_x=h(x) d(h(x))/dx

For example, lets look at cos²(x³). We have
f(x) = x²
g(x) = cos(x)
h(x) = x³
so
f(g(h(x)))= f(g(x³))=f(cos(x³))=[cos(x³)]² = cos²(x³)
and
d(f(g(h(x))))/dx = d(f(x))/dx|_x=g(h(x)) d(g(x))/dx|_x=h(x) d(h(x))/dx
=2x|_x=g(h(x)) sin(x)|_x=h(x) 3 x²
=2cos(x³) sin(x³) 3 x²
=6 x² cos(x³) sin(x³)
or, using the double angle formula,
f'(g(h(x))) = 3 x² sin(2 x³)

Now, for your problem and changing the notation a little, letting
f(x) = (1-4x)²
what can we use for f(x) and for g(x)? Is an h(x) needed?

 

[stapel]

I am having trouble differentiating the following function with respect to x.

h(x)=(1-4x)^2

Ive looked online for help and I keep seeing (chain rule). My question is, is there another name for the chain rule? or is there another method to differentiate this function? Ive searched my book and I cant find anything even similar to the chain rule. Ive also looked for similar examples in the book for differentiation and have come up with nothing.

What book are you using? :shock:

 

[MoShow]

Thanks a lot mate. Okay so this is what i got.

h(x)=(1-4x)^2 Let t=(1-4)x. therefore f(x)=t^2=2t. And g(x)=-4x=-4-0=-4
=2t(-4)
=-8(1-4x)
=-8+32x


I am using the book supplied by my tertiary provider. Engineering Mathematics - Describing change - an introduction to differential calculus.

 

[Ishuda]

Thanks a lot mate. Okay so this is what i got.

h(x)=(1-4x)^2 Let t=(1-4)x. therefore f(x)=t^2=2t. And g(x)=-4x=-4-0=-4
=2t(-4)
=-8(1-4x)
=-8+32x


I am using the book supplied by my tertiary provider. Engineering Mathematics - Describing change - an introduction to differential calculus.

Just a small typo, t=1-4x not (1-4)x and yes f(x)=t^2 but f'=2t and g'(x) = -4. Everything worked out for the correct answer

 

[MoShow]

Awesome, thanks a million.

 

[stapel]

I am using the book supplied by my tertiary provider. Engineering Mathematics - Describing change - an introduction to differential calculus.

I was hoping to be able to locate information online, so as to be able to point you toward helpful information inside your text, but I can't find any evidence of this book's existence! Did your teacher self-publish or something? :shock:

 

[Steven G]

I am having trouble differentiating the following function with respect to x.

h(x)=(1-4x)^2

Ive looked online for help and I keep seeing (chain rule). My question is, is there another name for the chain rule? or is there another method to differentiate this function? Ive searched my book and I cant find anything even similar to the chain rule. Ive also looked for similar examples in the book for differentiation and have come up with nothing.

any help will be greatly appreciated.

There is no need to formally use the chain rule here. The rule that handles this function is called the general power rule. It states that if y = [f(x)]^n, then y' = n[f(x)]^(n-1) * f'(x).
In your problem f(x) = 1-4x and n=2