y=(5x^4)ln(2x)

Question

Find the derivative 

Answer 1

y = 5x⁴ln(2x)

 

By the Product Rule, y' = 20x³ln(2x) + [2/(2x)](5x⁴)

 

                                = 20x³ln(2x) + 5x³

 

                                = 5x³(4ln(2x) + 1)

Answer 2

Use the product rule, and apply the chain rule when you take the derivative of ln(2x).

 

f = uv

u = 5x⁴

v = ln(2x)

 

f' = u'v + uv'

 

u' = 20x³  [power rule]

v' = [1/(2x)](2) = 1/x  [ln rule and chain rule]

 

f' = (20x³) [ln(2x)] + (5x⁴)(1/x)

 

f' = 20x³ln(2x) + 5x³

Answer 3

Hy Thanyaa,

 

Use the product rule for this problem

 

y' = 20x^3(ln(2x)) + 5x^4(1/2x)

 

y' = 20x^3ln(2x) + 5x^3 / 2