MAT 210 Arizona State University Calculus Questions

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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

– 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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