Find h'(x) when h(x)=g(2x+f(x^3)).

[nmwanta901]

Good afternoon!

I had recently taken a calc. quiz where one of the questions was to find h'(x) when h(x)=g(2x+f(x^3)) at a=1, as posted in the first picture, along with the table of values. Attached I have my work. However, I have seemed to have lost points on the problem where I multiply by 3x^2. I was told I needed to multiply by 3x^2 at some point, but it is just not in quite the right spot. I'm honestly really confused where I went wrong, I thought I went about using the chain rule correctly. Hopefully someone can spot where I went wrong and can point me in the right direction, as I really am kind of confused. Thanks for the help.

 

[Deleted member 4993]

Good afternoon!

I had recently taken a calc. quiz where one of the questions was to find h'(x) when h(x)=g(2x+f(x^3)) at a=1, as posted in the first picture, along with the table of values. Attached I have my work. However, I have seemed to have lost points on the problem where I multiply by 3x^2. I was told I needed to multiply by 3x^2 at some point, but it is just not in quite the right spot. I'm honestly really confused where I went wrong, I thought I went about using the chain rule correctly. Hopefully someone can spot where I went wrong and can point me in the right direction, as I really am kind of confused. Thanks for the help.
View attachment 22601

View attachment 22600

In your 2nd line of response:

You have....

[(2+F(x³)] * (3*x²)

It should be:

(2+[F(x³)] * 3*x²)

In other words only F(x³) should be multiplied by 3x²

 

[Steven G]

Your are multiplying the 2 by 3x^2! It should be 2+f'(x^3)*3x^2

 

[Steven G]

In your 2nd line of response:

You have....

[(2+F(x³)] * (3*x²)

It should be:

(2+[F(x³)] * 3*x²)

In other words only F(x³) should be multiplied by 3x²

Is F the same as f?

 

[Deleted member 4993]

Is F the same as f?

You'll need to ask that to the OP. In his handwritten answer - he uses 'F' instead of 'f'

 

[Steven G]

You'll need to ask that to the OP. In his handwritten answer - he uses 'F' instead of 'f'

The chart is extremely clear.

 

[nmwanta901]

Your are multiplying the 2 by 3x^2! It should be 2+f'(x^3)*3x^2

YES! That makes total sense, I see what happened now. I'm just glad it wasn't an error where I was way off, I realize know why it was wrong. And yes, in my post, I intended to use all lowercase "f's," just when I'm writing they sometimes look like a capital "F."

Thank you for the help!!

 

[nmwanta901]

In your 2nd line of response:

You have....

[(2+F(x³)] * (3*x²)

It should be:

(2+[F(x³)] * 3*x²)

In other words only F(x³) should be multiplied by 3x²

I see!!! Thank you much!!

 

[Deleted member 4993]

The chart is extremely clear.

Sure it is......

 

[HallsofIvy]

Personally, I was flummoxed when the problem said,
"Find h(x)= g(2x+ f(x^2)) at a= 1" since I had no idea how x depended on a!