find the derivative

Question

find the derivative

1.f(x)= 2x-7/3x-2

 

2. f(x)=(8x-9)^-4

 

3.d/dx-(^8 square rtt 8x^7-10)

 

4.find dy/dx for y=ln(2x^3-x^2)

Answer 1

The rules you need to apply here are the quotient rule, power rule, and most especially the chain rule.

 

1. I'm assuming this is (2x-7)/(3x-2)

The derivative of u/v is (uv' - u'v) / v².

Here, u = 2x-7 and v = 3x-2. u' = 2, v' = 3

Substitute and simplify to find the answer.

 

2. This is power rule/chain rule. The derivative of (g(x))ⁿ is n*(g(x))^n-1*g'(x)

Here, g(x) = 8x-9, n = -4, and g'(x) = 8.

 

3. The easiest way to take derivative of roots is to rewrite as exponents and use the power rule.

(8x⁷-10)^1/8

Again, power and chain rules; g(x) = 8x⁷-10, n=1/8, g'(x) = 56x⁶.

 

4. The derivative of ln(g(x)) = g'(x)/g(x)

You've got g(x) = 2x³ - x², g'(x) = 6x² - 2x

 

Please comment if you need more help!