1. ## Differentiate (x^2+3)^4

ok i know the answer is 4(x^2+3)^3(2x)

but i don't understand where did the (2x) come from

Why wouldn't it just be 4(x^2+3)^3 since the rule is d/dx X^n = nx^(n-1)

2. Originally Posted by jkami
ok i know the answer is 4(x^2+3)^3(2x)

but i don't understand where did the (2x) come from

Why wouldn't it just be 4(x^2+3)^3 since the rule is d/dx X^n = nx^(n-1)

Your rule is correct but you must also use the chain rule since your function is a function of a function!

Let's imagine that $g(x) = x^2+3$, and $f(x) = 4x^{3}$

Then your function can be written $h(x) = f(g(x))$

And the chain rule says that $h'(x) = f'(g(x)) \times g'(x)$

thx

4. ## Which one is correct?

differentiate

(x^3+9)^4

I got two answers from different sources

5. The first is correct.

The Chain Rule states, $\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$. The rule works because the rate of change of $g(x)$ multiplies the rate of change of $f(g(x))$. Hence, we have

$\frac{d}{dx}(x^3+9)^4 = 4(x^3+9)^3 \cdot 3x^2= 12x^2(x^3+9)^3.$

6. Originally Posted by jkami
differentiate

(x^3+9)^4

I got two answers from different sources

$\frac{d}{dx}(x^3+9)^4=\frac{d(x^3+9)^4}{d(x^3+9)}. \frac{d(x^3+9)}{dx}=4(x^3+9)^3.3x^2=12x^2(x^3+9)^3$