Find the derivative of the function. (Enter the logarithm function in the form log_a(b).)?

Question

s(x)=log_3(x^2+5x)

I dont understand what you did. Can you explain it to me?

Answer 1

Note: Derivative of log_a{u(x)}
= {1/ { u(x) * ln a} }* du/dx

amar missed the 'ln3'.

Edit:
The derivative of log_3(x) = 1/{ x*ln3 }

To answer the question s'(x) = 1/ { (x^2+5x)*ln3 } * (2x+5)
= 2x + 5 / { ln3 (x^2+5x) }

Answer 2

Let y = log (x² + 5x) where log is log to base 3.
Let u = x² + 5x
du / dx = 2x + 5
y = log u
dy/du = 1 / u
dy / dx = (dy / du) x (du / dx)
dy / dx = (1 / u ) X (2x + 5)
dy / dx = (2x + 5) / (x² + 5x)

Answer 3

s(x=log_3(x^2+5x)log_3+log(x^2+5x).

ds/dx=1/(x^2+5x) (2x+5).