differentiating functions: f(x)=5x^2ln(3x)

[Snow2021]

Hello all

Im struggling with some differentiating and want to know where to go next

The question i have is

f(x)=5x^2ln(3x) now i know i should be using the product rule so it should be f(x)*g'(x)+g(x)*f'(x)

so that should give me 5x^2*1/3+ln(3x)*10x

but when i have tried putting the same question into something like mathway my numbers dont represent the same and how do i go on to simplify this. Im trying to follow the books but i just can't get it to click in my head so maybe someone explaining it might be of more use

Regards
Snow

 

[Deleted member 4993]

Hello all

Im struggling with some differentiating and want to know where to go next

The question i have is

f(x)=5x^2ln(3x) now i know i should be using the product rule so it should be f(x)*g'(x)+g(x)*f'(x)

so that should give me 5x^2*1/3+ln(3x)*10x

but when i have tried putting the same question into something like mathway my numbers dont represent the same and how do i go on to simplify this. Im trying to follow the books but i just can't get it to click in my head so maybe someone explaining it might be of more use

Regards
Snow

g(x) = ln(3*x)

g'(x) = 1/(3*x) * 3 = 1/x

h(x)= x^2

h'(x) = 2*x

d/dx [5x^2 * ln (3x)]

=5[x^2 * (1/x) + 2*x * ln(3x)]

= 5[x + 2*x*ln(3x)]