1. ## differentiate

1. Differentiate the following with respect to x
a.
y=3/2x2
b.
y=ln (x3+x)
c.
y=ex/1n(3x)

can anyone manage this? good luckxx

2. Originally Posted by snappy23

1. Differentiate the following with respect to x
a. y=3/2x2
b. y=ln (x3+x)
c. y=ex/1n(3x)

can anyone manage this? good luckxx
1. I'm assuming the function is $\displaystyle y = \frac{3}{2x^2}$

rewrite as $\displaystyle y = \frac{3}{2}x^{-2}$ ... now use the power rule for derivatives.

2. derivative for the log of a function $\displaystyle y = \ln(u)$ ...

$\displaystyle y' = \frac{u'}{u}$

3. $\displaystyle y = \frac{e^x}{\ln(3x)}$ ... use the quotient rule

3. Originally Posted by snappy23
1. Differentiate the following with respect to x
a.
y=3/2x2
b.
y=ln (x3+x)
c.
y=ex/1n(3x)

can anyone manage this? good luckxx
Do you mean
a. y= (3/2)x^2?
If so, do you know the formula for the derivative of x^n: (x^n)'= nx^(n-1). That's usually one of the first formulas you learn.

b. y= ln(x^3+ x)?
Use the fact that the derivative of ln(x) is 1/x and the chain rule.

c. y= e^x/ln(3x)?
Use the fact that the derivative of e^x is e^x and the quotient rule.

4. Originally Posted by skeeter
1. I'm assuming the function is $\displaystyle y = \frac{3}{2x^2}$

rewrite as $\displaystyle y = \frac{3}{2}x^{-2}$ ... now use the power rule for derivatives.

2. derivative for the log of a function $\displaystyle y = \ln(u)$ ...

$\displaystyle y' = \frac{u'}{u}$

3. $\displaystyle y = \frac{e^x}{\ln(3x)}$ ... use the quotient rule
For a. i got y=3x/2x2 = 2x-2
dy/dx = 3x-2x -2 -1 = 6x-3 = 16/x3

did anyone else?
i can not do b or c. can anyone help there?