differentiate the equation Y= 3X4 (X2 +2)

Question

differentiate the equation. and show workings

 

Y= 3X⁴ (X² +2)

Answer 1

y = 3x⁴(x²+2)

 

y = 3x⁶ + 6x⁴

 

dy/dx = d(3x⁶)/dx + d(6x⁴)/dx

 

dy/dx = 18x⁵ + 24x³ = 6x³(3x² + 4)

Answer 2

You could do this using the product rule, but it would be easier to just multiply through first (distribute).

 

y=3x⁶+6x⁴

 

Then you can quickly use the power rule to get:

 

y=(6*3)x^6-1+(4*6)x^4-1

y=18x⁵+24x³