Question

F(x)= 7xln(x)
find y' and y"

Answer 1

Remember the product rule? Think of the first function as the 7x, and the other function as lnx\[\Large y = (7 x) \ln(x)\]
Derivative of 7x is 7, derivative of lnx is 1/x... from the product rule:
\[\Large y' = 7 \ln x + (7x) \frac{ 1 }{ x }\]

Answer 2

yeah, so it would be the same thing for quotient rule right. I had a lecture on finding the derivatives of logs but i did not understand them

Answer 3

is the second derivative 7/x

Answer 4

Derivative of a ln function is \[\Large \frac{ d }{ dx } \ln f(x) = \frac{ f \prime (x) }{ f(x) }\]
or the derivative of the inside function, divided by the inside function.

Answer 5

oh ok its the same thing as 1/f(x) * f'(x) right

Answer 6

Correct :)

for y'', you're right that it's 7/x. Since
\[\Large y' = 7 \ln x + (7x) \frac{ 1 }{ x } = 7 \ln x + 7\]

\[\large y \prime = 7 \ln x + 7\]
derivative of the 7 is just zero, so
\[\Large y \prime \prime = 7 \left( \frac{ 1 }{ x }\right)\]

Answer 7

ok thanks :)