find the derivative4 [Notes & HW Answers] 3.7 Implicit Functions [Prepwork 3.7] Q1. Which of the following points satisfies the equation 𝑥^2−𝑥𝑦^2=2? A: (1) (-2^(1/2)/2, (4.5)^(1/4)) ; (2) (-2^(1/2),0) Q2. (1) Find dy/dx when x^2 - xy^2 =2. A: (1) dy/dx = (y^2-2x)/-2xy (2) Find an equation for the tangent line to x^2 - xy^2 = 2 at the point (2,1). A: (2) y = (3/4)(x-2) + 1 Q3. Find all points satisfying the equation 𝑥2−𝑥𝑦2=2x2−xy2=2 where the tangent line is v.. 2022. 11. 21. [Notes & HW Answers] 3.6 The Chain Rule and Inverse Functions [Prepwork 3.6] Q1. Let 𝑔(𝑥)g(x) be an invertible, differentiable function with values given in the table below. 𝑥 2 5 8 𝑔(𝑥) 8 2 0 𝑔′(𝑥) -2 -0.25 -0.1 Find a formula for the tangent line of 𝑔^(−1)(𝑥) at 𝑥=2. A: y = -4(x-2)+5 Q2. Find the derivative of 𝑓(𝑥)=arctan(5ln(𝑥)). 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^.. 2022. 11. 21. [Notes & HW Answers] 3.4 The Chain Rule [Prepwork 3.4] Q1. The length,L, in micrometers (𝜇μm), of steel depends on the air temperature degrees celsius, and the temperature depends on time,t, measured in hours. If the length of a steel bridge increases by 0.25μm for every degree increase in temperature, and the temperature is increasing at 4 degrees celsius per hour, how fast is the length of the bridge increasing? A: At a rate of 1 μm.. 2022. 11. 21. [Notes & HW Answers] 3.2 The Exponential Functions [Prepwork 3.2] Q1. Let f (x) = x^10 +10^x. Find the first and second derivatives of f(x). A: f'(x) = 10x^9 + (ln 10)10^x ; f''(x) = 90x^8+(ln 10)(ln10)10^x Q2. For what value of a is y = 1+5x the tangent line for y = ax at x = 0? A: a = e^5 [HW 3.2] Q1. Find the derivative of y = 4x^8+8^x+12. A: dy/dx = 32x^7 + (ln 8)8^x Q2. Find the derivative of z = (ln 10)e^x. A: dz/dx = (ln 10)e^x. Q3. Find .. 2022. 10. 28. 이전 1 다음
