Differentiate the following functions:

(i) 6x⁵ + 4x³ – 3x² + 2x – 7

(ii)

(iii) ax³ + bx² + cx + d, where a, b, c, d are constants

(i) 6x⁵ + 4x³ – 3x² + 2x – 7

Formula:-

= n

Differentiating with respect to x,

6x⁵ + 4x³ – 3x² + 2x – 730x^5-1 + 12x^3-1 – 6x^2-1 + 2x^1-1 + 0

= 30x⁴ + 12x² – 6x¹ + 2x

(ii)

Formula:-

= n

Differentiating with respect to x,

=

=

(iii) ax³ + bx² + cx + d, where a, b, c, d are constants

Formula:-

= n

Differentiating with respect to x,

ax³ + bx² + cx + d) = 3ax^3-1 + 2bx^2-1 + c + d×0

= 3ax² + 2bx + c