How to find derivative?

Question

I need help to find the derivative of

1/ln(3t+5) with respect to t.

Please show steps. Thank you!

Answer 1

You need to remember two rules:

1) Chain Rule:

[f(g(x))]' = f'(g(x))*g'(x)

2)

[f(x)/g(x)]' = [f'(x)*g(x)-f(x)g'(x)]/[g(x)^2]  

Apply second rule and first when needed

[note {ln(3t+5)}'  = 1/(3t+5)*(3t+5)'=3/(3t+5) ]   :

y(x)=1/ln(3t+5)

=>

y'(x) = [-3/(3t+5)]/[(ln3t+5)^2]