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

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

babowmanjacob666

05.02.2022

h'(x)= $e^{x^{9}+In(x) } (9x^{8} +\frac{1}{x} )$

Step-by-step explanation:

h(x)= $e^{x^{9} +In(x)}$

first, we will use the chain rule

step1: we divide the function into two parts So,

f(x)= $e^{x^{9} +In(x)}$ and g(x)= $x^{9} +In(x)$

step2: rewrite $x^{9} +In(x)$ as u.

f(x)= $e^{u}$ and g(x)=u

step3: differentiate f(x) first.

f'(x)= $e^{u}$ (the formula is y= $e^{x}$ and y'= $e^{x}$ - the same)

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

f'(x)= $e^{x^{9}+In(x) }$ and g(x)= $x^{9}+In(x)$

step5: differentiate the function g(x).

g'(x)= $9x^{8} +\frac{1}{x}$

(for $x^{9}$ the formula is y= $x^{n}$ and y'= $nx^{n-1}$ ) (for In(x) the formula is y=In(x) and y'= $\frac{1}{x}$ )

step6: use the chain rule to finish out So,

h'(x)=f'(x) × g'(x)

= $e^{x^{9}+In(x) }$ × $9x^{8}+\frac{1}{x}$

step7: simplify.

h'(x)= $e^{x^{9} +In(x)}(9x^{8}+\frac{1}{x})$

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nsutton9985

12.08.2022

Step-by-step explanation:

Length:

l = w + 5

Perimeter

P = 2l + 2w = 2(w + 5) + 2w = 34 --> w = 6

l = 6 + 5 = 11

Solution

Width 6 feet and length 11 feet.

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