Differentiation, product rule?

Question

Differentiate with respect to x for the following expressions :
1) x^3 (1-3x^2)^4
2) (3x-4/x)^2 (1-x+7x^2)^4

Answer 1

1)
d( x³*(1-3x²)^4 )/dx =
3x²(1-3x²)^4 + x³*(-6x)*4(1-3x²)³ =
3x²(1-3x²)^4 - 24x^4*(1-3x²)³


2)
d( (3x-4/x)²(1-x+7x^2)^4 )/dx =
2(3+4/x²)(3x-4/x)(1-x+7x^2)^4 + 4(3x-4/x)²(14x)(1-x+7x^2)³ =
2(3+4/x²)(3x-4/x)(1-x+7x^2)^4 + (56x)(3x-4/x)²(1-x+7x^2)³

₢

Answer 2

(uv)' = u'v + uv'