# Math

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1. Simplify, and write in the base of 3: (9^x . 3^4x)^2
answer: 3^12x

2. Differentiate and simplify
a. y= 3x^4 - 4e^x + 8
answer: 4(3x^3 - e^x)

b. y= (3 + 4e^x)^5
answer: 20e^x (3+ 4ex)^4

c. y= (e^x - 1) / x^2
answer: (xe^x - 2e^x +2) / x^3

• Math -

y= 3x^4 - 4e^x + 8
dy/dx = 12 x^3 -4 e^x
= 4(3x^3 -e^x)

y = (3 + 4e^x)^5
Let u = 3+4e^x
y = u^5 dy/du = 5 y^4
dy/dx= dy/du*du/dx

dy/dx = 5(3 + 4e^x)^4*4e^x
= (20 e^x)(3 +4e^x)^4

You can do these. You won't learn without trying

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