Derivative help ASAP !!

[Dazed]

Can someone please help me with this by showing me step by step. Thanks

Find the derivative of these problems.

1. f(x) = [ln(15.7x^3)](e^15.7x^3)

I know the derivative of lnx is 1/x. I also know the derivative of e^x is e^x. I also know I need to use the product rule. So I know deriv. of prod function = (deriv of 1st function)(2nd function) + (1st function)(deriv of 2nd function)

Therefore, (1/(47.1x^2)(e^15.7x^3) + (ln(15.7x^3))(e^15.7x^3)

Is this right? If not, can u show me how to do it.


2. f(x) = 1/(x-2)^2*(3x^2-17x+4)

I don't know how to find the derivative of the 1st function. I think the 2nd function is 6x-17+0.

 

[wjm11]

Find the derivative of these problems.

1. f(x) = [ln(15.7x^3)](e^15.7x^3)

I know the derivative of lnx is 1/x. I also know the derivative of e^x is e^x. I also know I need to use the product rule. So I know deriv. of prod function = (deriv of 1st function)(2nd function) + (1st function)(deriv of 2nd function)

What you have stated is correct – but oversimplified. The derivative of ln(u) is (1/u)*(du/dx), and the derivative of e^u is e^u*(du/dx), where u is a function of x. Your derivative of the first function is incorrect. Let’s look at the first function a little differently than it appears:

ln(15.7x^3) = ln(15.7) + 3*ln(x)

That should make the derivative a bit more obvious: (3/x).
Your derivative of the second function is also incorrect. It should be

(e^15.7x^3)*(47.1x^2)

Therefore, f’(x) = (3/x)(e^15.7x^3) + (ln(15.7x^3))(e^15.7x^3)(47.1x^2)

 

[wjm11]

2. f(x) = 1/(x-2)^2*(3x^2-17x+4)

I don't know how to find the derivative of the 1st function. I think the 2nd function is 6x-17+0.

Once again, rewrite the first function in a different form to make the problem easier:

f(x) = 1/(x-2)^2 = (x-2)^(-2)
f’(x) = -2(x-2)^(-3)

Hope that helps.