Find the derivative: f(x)=(3^((4x^5)+x-8))*(log2(6x+3)) I'm not sure that my answer is correct. Thank's!

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You should use the product rule and the chain rule to differentiate the function with respect to x, such that:

`f'(x) = (3^((4x^5)+x-8))'*(log_2(6x+3)) + 3^((4x^5)+x-8))*(log_2(6x+3))'`

You need to convert the given logarithm to natural logarithm such that:

`log_2(6x+3) = (ln(6x+3))/(ln 2)`

`f'(x) = (3^((4x^5)+x-8)*ln 3*(4x^5+x-8)'*(log_2(6x+3)) + 3^((4x^5)+x-8))*(1/(ln 2))*((6x+3)')/(6x+3)`

`f'(x) = (20x^4+1)*ln...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

You should use the product rule and the chain rule to differentiate the function with respect to x, such that:

`f'(x) = (3^((4x^5)+x-8))'*(log_2(6x+3)) + 3^((4x^5)+x-8))*(log_2(6x+3))'`

You need to convert the given logarithm to natural logarithm such that:

`log_2(6x+3) = (ln(6x+3))/(ln 2)`

`f'(x) = (3^((4x^5)+x-8)*ln 3*(4x^5+x-8)'*(log_2(6x+3)) + 3^((4x^5)+x-8))*(1/(ln 2))*((6x+3)')/(6x+3)`

`f'(x) = (20x^4+1)*ln 3(3^((4x^5)+x-8)*((ln(6x+3))/(ln 2)) + 3^((4x^5)+x-8))*(1/(ln 2))*(6)/(6x+3)`

You should factor out `(3^((4x^5)+x-8))/(ln 2)`  such that:

`f'(x) = (3^((4x^5)+x-8))/(ln 2)((20x^4+1)*ln 3*ln(6x+3) + 6/(6x+3))`

Hence, evaluating the given derivative of the function yields `f'(x) = (3^((4x^5)+x-8))/(ln 2)((20x^4+1)*ln 3*ln(6x+3) + 6/(6x+3)).`

Approved by eNotes Editorial Team