Question

Find derivative of

a f(x)=2 x⁸ log _{3} / (2 x⁵ -9
b)f(x)=16 x⁷ log _{3}(2 x⁵ -9+{20 x¹² / {2 x⁵ -9) In 3}

Answer 1

To find the derivative of f(x) = 2x^8log_3(2x^5 - 9), you can use the product rule and the chain rule.

Step-by-step explanation:

To find the derivative of f(x) = 2x^8log_3(2x^5 - 9), we can use the product rule and the chain rule.

First, let's differentiate the first term, 2x^8. The derivative is 16x^7.

For the logarithmic term, the derivative is obtained by applying the chain rule. Let u = 2x^5 - 9. The derivative is du/dx = 10x^4. The derivative of logarithm base 3 is 1/(ln(3)u). Putting it together, the derivative of the log term is (1/(ln(3)(2x^5 - 9)))(10x^4).

Now we can combine the derivative of the first term 16x^7 with the derivative of the logarithmic term (1/(ln(3)(2x^5 - 9)))(10x^4) to find the overall derivative of f(x).