Please find the derivative and EXPLAIN how you got the answer. I’ve attached an example problem that shows how to do it (the answer to my question should be structured the same), but I’m a little unclear on the last steps, specifically where the “-1” in the numerator comes from.Find the derivative of the following function.

-9e2x

y =

8x + 3

Use the quotient rule to find the derivative of the function.

The quotient rule states that only

d[ f(x) g(x)f'(x) – f(x)g'(x)

dx L g(x)

[g(x)?

Let f(x) = -9 e 2x and g(x) = 8x +3 so that g'(x) = 8.

The chain rule can be used to find f'(x).

oby (eks) =ke ky

f'(x) = (- 9) (e 2x) + (2x) (-9)

= (-9)(2 e 2x) + (e 2x) (0)

Product Rule

Chain Rule

– 18 e 2x

Now use the quotient rule.

d

dx

– 9e 2x

)

8x +3

(8x+ 3)(-9e2a) – (-9e23) S(x + 3)

(8x+32

(8x+ 3) (-18 e2) – ( – 9e 2) (8)

(8x+ 32

Simplify.

d

– 9e 2x

없

– 18 e2×(8x-1)

(8x+ 32

dx

8x+ 3

Question is complete.

Find the derivative of the following function.

8 e 8x

y =

5x-2

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