Question

find the derivative of y = 8t^4ln(7t)

I know i have to use the product rule but i cant figure this out

Answer 1

well, let's choose f(x) = x^4 and g(x) = log(7x), by the product rule the derivative of f(x)*g(x) is the derivative of f(x) times g(x) plus the derivative of g(x) times f(x), the derivative of f(x) is the power rule, and the derivative of log(7x) is a little more tricky - you have to apply the chain rule

Answer 2

ok i feel like i answer all of these the same way i dont know what im doing wrong though

Answer 3

i got 32t^3ln(7t) + (8t^3)/7

Answer 4

and thats not log its natural log

Answer 5

it's a little more complicated than that, but yes.

Answer 6

then what am i doing wrong. that wasnt right either

Answer 7

ok, lets go through it again. f'(x)*g(x) + g'(x)*f(x). f'(x) = 4t^3 and g'(x) is by the chain rule, 7*1/x by definition. so this becomes 4x^3 * log(7x) + x^4*7*1/x and that whole thing multiplied by 8