Chapter 5 Homework

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Question

Chapter 5 Homework

1. True or False

The derivative of

g (t) = \sqrt{t} e^{- 2 t}

g ‘ (t) = \frac{1}{2 \sqrt{t}} - \frac{2}{e^{2 t}}

2. Find the derivative of

f (x) = x e^{- x^{2}}

3. Find the derivative of

f (x) = x^{2} e^{x} + e^{x}

4. True of False

The derivative of

f (x) = \ln (e^{x^{2}} + 1) i s

$f ‘ (x) = \frac{2 x e^{x^{2}}}{e^{x^{w}} + 1}$

5. True or False

The derivative of

f (x) = \frac{\ln x}{x + 1} i s f ‘ (x) = \frac{1}{x (x + 1)}

Type in your simplified answer below after you

Use logarithmic differentiation to find the derivative of

$f (x) = (2 x^{3} + 1) {(x^{2} + 2)}^{3}$

Type in your simplified answer below after you

Use logarithmic differentiation to find the derivative of

$f (x) = \frac{x {(x^{2} - 2)}^{2}}{x - 1}$

8. Find an equation of the tangent line to the graph of

y = e^{- 2 x} a t t h e p o i n t (1, e^{- 2})

9. Find an equation of the tangent line to the graph of

y = x e^{- x} a t t h e p o i n t (1, e^{- 1})

10. Find the present value of $30,000 due in 5 years at an interest rate of 5% / year compounded monthly.

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This question is taken from Math 238 – Calculus for Business and Social Sciences » Spring 2022 » Homeworks

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