Differentiate the function.
h(x) = e^x^9+In(x)

h'(x)=

Step-by-step explanation:

h(x)=

first, we will use the chain rule

step1: we divide the function into two parts So,

f(x)=   and  g(x)=

step2: rewrite as u.

f(x)=    and   g(x)=u

step3: differentiate f(x) first.

f'(x)=   (the formula is y= and y'= - the same)

step4: write the value of u for each function but now sub it in the differentiable form of f(x).

f'(x)=  and g(x)=

step5: differentiate the function g(x).

g'(x)=

(for the formula is y= and y'= ) (for In(x) the formula is y=In(x)  and y'= )

step6: use the chain rule to finish out So,

h'(x)=f'(x) × g'(x)

= ×

step7: simplify.

h'(x)=

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i