Final answer:
The derivative of the function 2ᵂᵗ³x-5 ᵗᵈ⁴(6x) is found by applying differentiation rules, resulting in 6ᵂᵗ²x (-ᵍᵉᵖ) -120 ᵗᵈ³(6x).
Step-by-step explanation:
The question asks for the derivative of the function 2ᵂᵗ³x-5 ᵗᵈ⁴(6x). To find the derivative, we apply the rules of differentiation, specifically the power rule, the chain rule, and the product rule for differentiation.
First, we find the derivative of 2ᵂᵗ³x, which is 6ᵂᵗ²x · (-ᵍᵉᵖ). Next, we differentiate -5 ᵗᵈ⁴(6x) using the chain rule; the derivative is -20 ᵗᵈ³(6x) · 6, simplified to -120 ᵗᵈ³(6x). Combining these results gives the final derivative of the function as 6ᵂᵗ²x · (-ᵍᵉᵖ) -120 ᵗᵈ³(6x).