Question

Write a derivative formula for the function f(x) =12.9(4.9ˣ)/x² f'(x)=

Answer 1

The derivative of the given function is (12.9 * (ln(4.9) * 4.9ˣ) * x² - 12.9 * (4.9ˣ) * 2x) / x⁴.

Step-by-step explanation:

The given function is f(x) = 12.9 * (4.9ˣ) / x². To find the derivative of this function, we can use the quotient rule.

The quotient rule states that if we have a function u(x)/v(x), then the derivative of the function is (u'(x)v(x) - u(x)v'(x)) / v(x)².

For the given function, u(x) = 12.9 * (4.9ˣ) and v(x) = x². Taking the derivatives, we have u'(x) = 12.9 * (ln(4.9) * 4.9ˣ) and v'(x) = 2x.

Substituting these values into the quotient rule, we get f'(x) = (12.9 * (ln(4.9) * 4.9ˣ) * x² - 12.9 * (4.9ˣ) * 2x) / x⁴.