1. ## respect to x

2. Differentiate the following functions with respect to
x:
(a)
y = 3x^4

(b)
y = 3 sin(2x)

Hint: Use the chain–rule with
u = 2x.

2. Originally Posted by marikas

2. Differentiate the following functions with respect to
x:
(a) y = 3x^4
(b)

y = 3 sin(2x)
Hint: Use the chain–rule with

u = 2x.
You have a hint. Why not use it.

a) 12x^3
b) 6cos(2x)

You REALLY can't do these? You may need to have a serious chat with your academic advisor.

3. C'mon TKHunny, remember that some people are not as smart as you.

Originally Posted by marikas

2. Differentiate the following functions with respect to
x:

(a) y = 3x^4
(b)

y = 3 sin(2x)

Hint: Use the chain–rule with

u = 2x.
For letter a), you need to know that $\displaystyle (x^n)'=nx^{n-1},$ for $\displaystyle n$ a rational number.

For letter b), I'll use two ways:

$\displaystyle y'=3\cos(2x)\cdot(2x)'=3\cos(2x)\cdot2=6\cos2x.$

--

Define $\displaystyle u=2x\implies u'=2.$ Since $\displaystyle y=3\sin u\implies y'=3\cos u\cdot u'.$

Now back substitute

$\displaystyle y'=3\cos2x\cdot2=6\cos2x.$

Hope it helps