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
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.