Help me with Derivatives Logarithmic?

Question

In(tan(x))

I got 1/(tan(x)(cos(x)^2)), don't know it was correct or not.

Answer 1

the answer is correct

Answer 2

The trick with solving differentials of logarithmic functions is to do it in two parts.

If you have to differentiate ln(f(x)), where f(x) is any function of x, then you can begin by replacing the function by a variable (often, we use u)

Here, we set u = tan(x)

Differential of ln(u) = (1/u) * du

change u back to tan(x)

(1/tan(x)) * d(tan(x))
You are left with finding the differential of tan(x) and multiplying through.

Answer 3

The way that I differentiate natural log is the following:

The "inside" function is tan(x)

The "outside" function is ln(x)

By chain rule, when the ln(x) is the outside function, the derivative is always "the derivative of the inside divided by the inside"

derivative of tan(x) divided by tan(x)

sec^2 (x) / tan(x) which written in terms of cosine is what you got.

Answer 4

u r right