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Suppose that f(x) and g(x) are differentiable functions such that f(1) = 2, f'(1) = 4,...

Question:

Suppose that f(x) and g(x) are differentiable functions such that {eq}f(1) = 2, f'(1) = 4, g(1)=5,\space \text{and} g' (1)= 3 {/eq}. Find {eq}h' (1) {/eq} when {eq}h(x)=\frac{f(x)}{g(x)} {/eq}.

Quotient Rule:

The quotient rule determines the derivative of a ratio via a differentiation formula involving both the sub-functions and their derivatives.

To implement the quotient rule, we follow the following equation:

{eq}\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\left(\frac{b(x)}{c(x)}\right)= \frac{c(x)b'(x) - b(x)c'(x)}{(c(x))^2} {/eq}

Answer and Explanation:

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The quotient rule applied to {eq}h(x) {/eq} gives us {eq}h'(x) {/eq}.

Furthermore, we'll substitute {eq}x=1 {/eq} to get what we need:

{eq}\begin...

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Quotient Rule: Formula & Examples

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Chapter 1 / Lesson 5
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What is the quotient rule? Read the definition of quotient rule and see the quotient rule formula, and practice applying it with some quotient rule examples.


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