Differentiate y = 7x(9x^4 - 8x)?

Question

Can you please break it down.

Answer 1

 By Distributive law  Y= 7x(9x⁴) - 7x ( 8x )

   Y = 63x⁵ - 56x²

Differentiate each side with respective x  

dy/dx = d/dx ( 63x⁵ - 56x²)

dy/dx = d/dx ( 63x^{5 )} - d/dx (56x²)

 Recall: Constant multiply rule: d/dx(axⁿ)=ad/dx(xⁿ)

dy/dx = 63 ( d/dx (x⁵)) - 56 d/dx ( x² )

 Recall: The power rule

d/dx(xⁿ)= nx^(n-1) 

substitute above formula in the differential equaqtion

dy/dx = 63 ( 5x^5-1) - 56 ( 2x^2-1 )

Simplify the above equation

dy/dx = 315x⁴ - 112x¹

dy/dx= 315x⁴ - 112x

The differentiate of the above equation dy/dx = 315x⁴ - 112x.