1. ## derivitives

a) $\displaystyle f(x)=1/sin(x)$
b) $\displaystyle g(x)= ln(x^2)$

find the derivitives....just need to confirm.

i have worked through the questions and i for a) i get $\displaystyle (-cos(x))/sin(x)^2$ by using the quotient rule. but when i try differentiate on a computer software i get $\displaystyle -1/sin(x)^2*cos(x)$....are they the same????

and for the second one i know that the answer is $\displaystyle 2/x$since ln(x) = 1/x. but not sure how to show the working...any help would be appreciated.

thanks

2. Originally Posted by b00yeah05
a) $\displaystyle f(x)=1/sin(x)$
b) $\displaystyle g(x)= ln(x^2)$

find the derivitives....just need to confirm.

i have worked through the questions and i for a) i get $\displaystyle (-cos(x))/sin(x)^2$ by using the quotient rule. Mr F says: Correct.

but when i try differentiate on a computer software i get $\displaystyle -1/sin(x)^2*cos(x)$....are they the same???? Mr F says: Yes. $\displaystyle -\frac{1}{\sin^2 x} \times \cos x = -\frac{\cos x}{\sin^2 x}$.

and for the second one i know that the answer is $\displaystyle 2/x$since ln(x) = 1/x. but not sure how to show the working...any help would be appreciated.

thanks
For the second one, you could use the fact that $\displaystyle \ln x^2 = 2 \ln x$. And you know the derivative of $\displaystyle \ln x$ .....

Recall log rule: $\displaystyle \ln a^n = n \ln a$.