Question

Find the derivative of the function. z = 3t¹³/³ − 2t⁷/⁴ − t¹/²+ 6 z'=

Answer 1

To find the derivative of the function z = 3t¹³/³ − 2t⁷/⁴ − t¹/²+ 6, we can use the power rule, which states that if f(x) = x^n, then f’(x) = nx^(n-1). We can apply this rule to each term of the function, and then simplify the result. The derivative is:

z’ = 3(13/3)t^(13/3 - 1) - 2(7/4)t^(7/4 - 1) - (1/2)t^(1/2 - 1) + 0

z’ = 13t^(10/3) - (7/2)t^(3/4) - (1/2)t^(-1/2)

z’ = 13t^(10/3) - (7/2)t^(3/4) + (1/2)t^(-1/2)

This is the final answer.

: [Power Rule]

Explanation: