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1.Find the derivative of the following function using the definition of the derivative (first principle).

• 𝑦=4𝑥2−12𝑥+40

• 𝑔(𝑡)=𝑝𝑝+2

2.A camera is located 50 feet from a straight road along which a car is traveling at 100 feet per second. The camera turns so that it is pointed at the car at all times. In radiant per second, how fast is the camera turning as the car passes closest to the camera?

3.Differentiate the following functions 𝑦=𝑥6−4𝑥2+2𝑥+14

𝑦=𝑒3𝑥3

𝑦=4(4−𝑥)3

4.Differentiate the following functions 𝑦=𝑠𝑖𝑛3𝑥

𝑦=3𝑡𝑎𝑛 (𝑥+3)

𝑦=6𝑐𝑜𝑠3𝑥

5.Differentiate the following functions 𝑦=5𝑥21−𝑥

𝑦=𝑥𝑥+3

𝑦=3𝑥2+4𝑥+3𝑒𝑥

6.Differentiate the following functions 𝑦=(𝑥−4)3(𝑥+3)1

𝑦=(𝑥−4)3(𝑥+3)

𝑦=√𝑥+2(𝑥−2)2Type equation here.

7.Find the first four derivatives for each of the following

𝑦=3𝑥2+8𝑥1/2+𝑒𝑥

𝑦=𝑐𝑜𝑠𝑥

𝑦=𝑙𝑛 (1+𝑡2)

8.Find for the following functions

𝑥3𝑦5+4𝑥=7𝑦3+2

2𝑥2+2𝑦2=10

9.Find the gradient function of the tangent line to the parametric curve given by

• 𝑥=3𝑠𝑖𝑛𝜃, 𝑦=𝑐𝑜𝑠2𝜃.

• 𝑥=𝑏(𝜃−𝑠𝑖𝑛𝜃), 𝑦=𝑏(1−𝑐𝑜𝑠𝜃).

10.A cylindrical can is to be made to hold 2L of oil. Find the dimensions that will minimize the cost of metal to manufacture the can

**Title:**
Engineering Mathematics

**Length:**
2 pages
(550 Words)

**Style:**
MLA

**Preview**

**Engineering Mathematics**

**Question One Answer:**

- Y=4x
^{2}-12x+40. The formula for first principle of differentiation is y¢=. Since y=4x^{2}-12x+40, then y(x+Dx)=4(x+Dx)^{ 2}-12(x+Dx) +40. This is equivalent to y(x+Dx) =4x^{2}+8xDx +4Dx^{2}-12x-12Dx +40. Substitute it in the formula.

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