Suppose that f and g are differentiable functions such that

Suppose that f and g are differentiable functions such that f(3)=4, g(3)=2, f\'(3)=-6, and g\'(3)=5.
Let h(x)=f(x) times g(x) and let k(x)=f(x)/f(x)-g(x).
a) calculate h\'(3)
b)calculate k\'(3)
Please show your work

Given
h(x)=f(x)g(x)
Then
h\'(x)=f(x)g\'(x)+f\'(x)g(x)
Thus
h\'(3)=f(3)g\'(3)+f\'(3)g(3)=4*5+(-6)(2)=20-12=8
k(x)=f(x)(f(x)-g(x))^-1

Then

k\'(x)=f\'(x)(f(x)-g(x))^-1+f(x)(-1)(f(x)-g(x))^-2(f\'(x)-g\'(x))

Thus

k\'(3)=f\'(3)(f(3)-g(3))^-1+f(3)(-1)(f(3)-g(3))^-2(f\'(3)-g\'(3))

=-6((4-2)^-1+4(-1)(4-2))^-2(-6-(5))

=-3+2(11)=19

$Suppose that f and g are differentiable functions such that f(3)=4, g(3)=2, f\'(3)=-6, and g\'(3)=5. Let h(x)=f(x) times g(x) and let k(x)=f(x)/f(x)-g(x). a) ca$

Suppose that f and g are differentiable functions such that

Solution

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