- f′(x) =
The rule for finding the derivative of y = ln u is , where u is a function of x. Here u
= x^4 + 8. Therefore, the derivative is f′(x) = = .
- f′(x) =
The rule for finding the derivative of y = ln u is , where u is a function of x.
Before we find the derivative, we can use the laws of logarithms to expand the logarithm. This
way, we won’t have to use the Product Rule. We get ln(3x ) = ln 3 + ln x + ln =
ln 3 + ln x + ln(3 + x). Now we can find the derivative: f′(x) = 0 + =
.
- f′(x) = csc x
The rule for finding the derivative of y = ln u is , where u is a function of x.
Here u = cot x − csc x. Therefore, the derivative is f′(x) = (− csc^2 x + csc x cot
x). This can be simplified to: f′(x) = = csc x.
- f′(x) =
The rule for finding the derivative of y = ln u is , where u is a function of x.
Before we find the derivative, we can use the laws of logarithms to expand the logarithm. This
way, we won’t have to use the Product Rule or the Quotient Rule. We get ln = ln
5 + ln x^2 − ln = ln 5 + 2 ln x − ln (5 + x^2 ). Now we can find the derivative: f′(x) =
