Example 13: Find the derivative of f(x) = πsinx.
f′(x) = πsinx (cos x) ln πFinally, here’s every nasty teacher’s favorite exponential derivative.
Example 14: Find the derivative of f(x) = xx.
First, rewrite this as f(x) = e x ln x. Then, take the derivative.
f′(x) = ex ln x = ex ln x (ln x + 1) = xx(ln x + 1)Would you have thought of that? Remember this trick. It might come in handy! Okay. Ready for some
practice? Here are some more solved problems. Cover the solutions and get cracking.
PROBLEM 1 . Find the derivative of y = 3ln(5x^2 + 4x).
Answer: Use Rule No. 2.
PROBLEM 2. Find the derivative of f(x) = ln(sin(x^5 )).
Answer: Use Rule No. 2 in addition to the Chain Rule.
f′(x) = = 5x^4 cot(x^5 )PROBLEM 3. Find the derivative of f(x) = e^3 x
(^7) − 4x 2
.
Answer: Use Rule No. 4.
f′(x) =(21x^6 − 8x)e^3 x
(^7) − 4x 2
PROBLEM 4. Find the derivative of f(x) = log 4 (tan x).
Answer: Use Rule No. 6.
f′(x) =
PROBLEM 5 . Find the derivative of y = log 8.