For some functions f and g, f' (2) = 3 and g' (2) = 5. Calculate h'(2) when (a) h (x) = g (x) - f...


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}.


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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We are given the derivatives,

{eq}\bullet \; f'(2)=3 {/eq},

{eq}\bullet \; g'(2)=5 {/eq}.

Question (a)

If we define the function,


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Learn more about this topic:

Applying the Rules of Differentiation to Calculate Derivatives


Chapter 8 / Lesson 13

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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