For some functions f and g, f' (2) = 3 and g' (2) = 5. Calculate h'(2) when (a) h (x) = g (x) - f...
Question:
For some functions {eq}\displaystyle f {/eq} and {eq}\displaystyle g, \ f' (2) = 3 {/eq} and {eq}\displaystyle g' (2) = 5 {/eq}. Calculate {eq}\displaystyle h'(2) {/eq} when
(a) {eq}\displaystyle h (x) = g (x) - f (x) {/eq}.
(b) {eq}\displaystyle h (x) = 2 f(x) + g(x) {/eq}.
(c) {eq}\displaystyle h (x) = 11 g (x) + 1.76 {/eq}.
Derivation
The derivative of a function is by definition the limit when {eq}\Delta x\rightarrow 0 {/eq} of the ratio,
{eq}\lim_{\Delta x\rightarrow 0}\dfrac{f(x+\Delta x)-f(x)}{\Delta x} {/eq}.
The derivative rules are useful to find the derivative of elementary functions. The derivation is a lineal operation, therefore, the derivation of the algebraic sum of two functions is the algebraic sum of the derivatives.
Answer and Explanation:
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View this answerWe are given the derivatives,
{eq}\bullet \; f'(2)=3 {/eq},
{eq}\bullet \; g'(2)=5 {/eq}.
Question (a)
If we define the function,
{eq}h(x)=g(x...
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Chapter 8 / Lesson 13The 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.