Math derivative

Question

y= 7x - ln(4x³)

y= log₇(5x)

Answer 1

For this you would want to use differentiation in which you would do this.

d/dx (7x) - d/dx (ln(4x^3))

The derivative of 7x is 7

Then you have the remainder of the problem you have to derive in which you would do this where the differentiation is applied. You will be using (d/dx) ln(u) = 1/u * du/dx. Anytime you have a log you put 1 over the log.

du/dx (ln(4x^3)) * 1/u (1/4x^3)

this will be 12x^2 * 1/4x^3

you can reduce this which will be 3/x.

After this you have 7 - 3/x as the derivative.

The second one you will also use differentiation. Here you can do

1/5x ln 7 * d/dx(5x)

1/5x ln 7 * 5

Then combine

5/5x ln7 is

1/x ln7