The functions f(x) and g(x) are differentiable. The function h(x) is defined as: h(x)= (f(x))/(g(x)) If f(-1)= 6, f'(-1)= -3, g(-1)= 2, and g'(-1)= 5, what is h'(-1)? Simplify any fractions. h'(-1)= _____

Question

Bytelearn · Accepted Answer

Quotient rule for differentiation: To find h'(-1), we need to use the quotient rule for differentiation, which states that if h(x) = f(x)/g(x), then h'(x) = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2. We will apply this rule using the given values for f(-1), f'(-1), g(-1), and g'(-1).Calculate the numerator: First, we calculate the numerator of the derivative using the values provided: g(-1)f'(-1) - f(-1)g'(-1) = (2)(-3) - (6)(5).Perform multiplication: Performing the multiplication, we get: (2)(-3) - (6)(5) = -6 - 30 = -36.Calculate the denominator: Next, we calculate the denominator of the derivative, which is (g(-1))^2. Since g(-1) = 2, we have (2)^2 = 4.Find h'(-1): Now we can put together the numerator and the denominator to find h'(-1): h'(-1) = (-36) / (4).Divide to get the final result: Dividing -36 by 4 gives us h'(-1) = -9.

The functions $f(x)$ and $g(x)$ are differentiable. $\newline$ The function $h(x)$ is defined as: $h(x)= \frac{f(x)}{g(x)}$ $\newline$ If $f(-1)= 6$ , $f'(-1)= -3$ , $g(-1)= 2$ , and $g'(-1)= 5$ , what is $h'(-1)$ ? $\newline$ Simplify any fractions. $\newline$ $h'(-1)=$ _____

Full solution

More problems from Even and odd functions

Related topics