# 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.

Become a Study.com member to unlock this answer!

We 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...