[calc] multiplication issue?

[u/lillonghornlad]

The correct answer to this derivative is 3/2(sqrt3x+4). I just don’t know where in the work I was supposed to multiply by three or how that works into the equation. Thanks for the help in advance!

[u/Roshi_AC]

Google chain rule

[u/lillonghornlad → u/Roshi_AC]

We hadn’t learned about that in class yet so I didn’t know that rule existed

[u/jimlikesmath]

Most have already mentioned the chain rule. I'm just going to point out something small, but important. When you rewrite the expression, that should be labeled as f(x), not f'(x). We can't label the function as the derivative until we've taken the derivative.

[u/Historyofspaceflight → u/jimlikesmath]

This bothered me too

[u/lillonghornlad → u/Historyofspaceflight]

Okay well I’m VERY new to calculus

[u/Roshi_AC → u/jimlikesmath]

That’s a good point, good eye.

[u/Famous_Limit_5352]

You’ve essentially differentiated with respect to 3x+4, so by the chain rule, you need to multiply the answer by its derivative.

[u/Alkalannar]

Chain rule.

You need to multiply by the derivative of 3x + 4, which is...3.

[u/JanetInSC1234]

f'(x) = (1/2) (3x + 4) ^-1/2 times the derivative of the inside of the ( ).

So,f'(x) = (1/2)(3x + 4) ^-1/2 (3) = (3/2) (3x + 4) ^-1/2

Your numerator should have a 3, not 1.

[u/bumbatafata]

Line #2 is wrong, that's not the derivative. That's a rewriting of the same function to get you ready to apply the chain rule. So you shouldn't call it f'(x) as that is still f(x)

And as to your mistake, you didn't apply chain rule properly. You didn't multiply by the derivative of the inner function 3x+4 which would be 3 and that's how you get the 3 on the top.

[u/[deleted]]

Multiply by derivative of the inside function

[u/cin670]

Chain rule: d/dx[f(g(x)] = f’(g(x)) • g’(x)

The g’(x) is the derivative of g(x) = 3x + 4, which is 3.

[u/MedPhys90]

You forgot to take the derivative of what’s inside the parentheses

[u/Icy_Butterfly8443]

What’s calc is that some sort of slang?

[u/lillonghornlad → u/Icy_Butterfly8443]

Pretty obviously short for calculus lol

[u/NumerousSense1820]

Remember the rule for derivatives like this is derivative of the outside function (which is what you did first), multiplied by the derivative of the inside function

[u/InatuAtu → u/NumerousSense1820]

Show your work. Try writing it as follows and it might help you.

dy/dx = (dy/du)(du/dx) where you substitute u for the inner term part of the chain rule.

This shows you algebraically why you need to use the chain rule.

Sometimes it’s easier to see what’s going on by writing it out as dy/dx instead of f’(x).

If you need more clarification just let me know.

[u/justastudent_here]

must multiply with 3 as it is the derivative of 3x+4, then your answer will be correct

[u/InevitableLungCancer]

In addition to the chain rule, rationalize the denominator and factor out 3 from the top and the bottom:

sqrt(3x+4)/(2x+8/3)

[u/Immediate_Turnip9406]

Where chain rule?

[u/unidentified2202]

You are supposed to use the Chain rule

[u/RangeRoverRover]

You cant use the power rule if the function is a composite function

[u/LibAnarchist]

This is called the chain rule. Suppose we have two differentiable functions, f, g. The derivative (g(f(x)))' ≠ g'(f(x)). It is in fact f'(x) g'(f(x))

[u/nerdy_things101]

Chain rule….

[u/TheFunnybone]

Chain chain chain, chain of rules