

[Prepwork 3.6]
Q1. Let ๐(๐ฅ)g(x) be an invertible, differentiable function with values given in the table below.
๐ฅ | 2 | 5 | 8 |
๐(๐ฅ) | 8 | 2 | 0 |
๐โฒ(๐ฅ) | -2 | -0.25 | -0.1 |
Find a formula for the tangent line of ๐^(โ1)(๐ฅ) at ๐ฅ=2.
A: y = -4(x-2)+5

Q2. Find the derivative of ๐(๐ฅ)=arctan(5ln(๐ฅ)).
A: f'(x) = 5/(x*(25*ln^2(x)+1)

[HW 3.6]
Q1. Find the derivative of the function f(t), below.
f(t) = ln(t^9 +8)
A: f'(t) = 9t^8/(t^9+8)

Q2. Find the derivative of the function j(x), below. Assume that n and p are constants.
A: j'(t) = ne^(nx) / (e^(nx) + p)

Q3. Find the derivative of the function f(y), below. It may be to your advantage to simplify before differentiating.
f(y) = arcsin(y^2)
A: f'(y) = 2y/(1-y^4)^(1/2)

Q4. Find the derivative of the function g(t), below. It may be to your advantage to simplify before differentiating.
g(t) = tan(ln(t))
A: g'(t) = 1/(cos^2(ln(t))*t

Q5. Find the derivative of the function h(w), below. It may be to your advantage to simplify before differentiating.
h(w) = 8w*arcsin(w)
A: h'(w) = 8*arcsin(w) + 8w* (1/(1-w^2))

Q6. Find the derivative of the function f(t), below.
f(t) = ln(ln(4t)) + ln(ln7)
A: f'(t) = 1/t*ln(4t)

'[Umich] COE Core > MATH 115 (Calc 1)' ์นดํ ๊ณ ๋ฆฌ์ ๋ค๋ฅธ ๊ธ
[Notes & HW Answers] 3.9 Linear Approximation (0) | 2022.11.21 |
---|---|
[Notes & HW Answers] 3.7 Implicit Functions (0) | 2022.11.21 |
[Notes & HW Answers] 3.5 The Trigonometric Functions (0) | 2022.11.21 |
[Notes & HW Answers] 3.4 The Chain Rule (0) | 2022.11.21 |
[Notes & HW Answers] 3.3 The Product and Quotient Rules (0) | 2022.10.30 |
๋๊ธ