Cracking The Ap Calculus ab Exam 2018

Example 2: Find the derivative of f(x) = ln(5x − 3x^6 ).

f′(x)   =   

Example 3: Find the derivative of f(x) = ln(cos x).

f′(x)   =       =   −tan    x

Finding the derivative of a natural logarithm is just a matter of following a simple formula.

THE DERIVATIVE OF ex

As you’ll see in Rule No. 3, the derivative of ex is probably the easiest thing that you’ll ever have to do in
calculus.

Rule    No. 3:  If  y   =   ex, then        =   ex

That’s not a typo. The derivative is the same as the original function! Incorporating the Chain Rule, we get
a good formula for finding the derivative.

Rule    No. 4:  If  y   =   eu, then        =   eu

And you were worried that all of this logarithm and exponential stuff was going to be hard!

Example 4: Find the derivative of f(x) = e^3 x.

f   (x) =   e^3 x(3)    =   3e^3 x

Example 5: Find the derivative of f (x) = ex

3

.

f′(x)   =   ex

3

    (3x^2 ) =   3x^2 ex

3

Example 6: Find the derivative of f (x) = etanx.