a) Find all functions f such that f'(x) = 1 for all x. b) For a differentiable function g, find...
Question:
a) Find all functions f such that f'(x) = 1 for all x.
b) For a differentiable function g, find an expression for(1/g)' (x).
c) Let h be a differentiable function such that h'(x) = h{eq}^2 {/eq}(x) for all x (this is known as a differential equation). Find (1/h)' (x).
d) Using the result in (a), find all possible functions h satisfying the equation in (c).
Application of Differentiation:
Some times we use differentiation to obtain a function when it's derivative is known to us. All we need to just integrate the derivative of the function and do some manipulation will lead to the original function. We can also find derivative of the reciprocal of the function by simple differentiation method.
Answer and Explanation: 1
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Given:
- For a function {eq}f {/eq} it is given that {eq}f'\left( x \right) = 1 {/eq} all {eq}x {/eq}.
a)
We have {eq}f'\left( x \right) =...
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Applying the Rules of Differentiation to Calculate Derivatives
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Chapter 8 / Lesson 13
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The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples.
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