Question

Find the derivative of h(z) = (b/(a x²))⁵ assume a and b are constant?

Answer 1

To find the derivative of h(z) = (b/(a x²))⁵, we use the power rule and chain rule for derivatives. The derivative is -10b²/(a² x⁵).

Step-by-step explanation:

To find the derivative of h(z) = (b/(a x²))⁵, we can use the power rule and chain rule for derivatives. The power rule states that if we have a function raised to the power n, the derivative is given by n times the function raised to the power n-1 times the derivative of the function. The chain rule states that if we have a composite function, the derivative is given by the derivative of the outer function multiplied by the derivative of the inner function.

Applying these rules, we have:

h'(z) = 5(b/(a x²))⁴ * (b/(a x²))' = 5(b/(a x²))⁴ * (-2b/(a x³)) = -10b²/(a² x⁵)