DERIVATIVE OF POLYNOMIALS

Find the derivative if:

Problem 1 :

f(x) = ax³ + bx² + cx + d

Solution :

f(x) = ax³ + bx² + cx + d

f’(x) = 3ax^(3-1) + 2bx^(2-1) + c + 0

f’(x) = 3ax² + 2bx + c

Problem 2 :

k = 1/a (x² + b/x + c)

Solution :

k = 1/a (x² + b/x + c)

dk/dx = 1/a (2x + bx^-1 + 0)

= 1/a (2x + (-bx^(-1-1))

= 1/a (2x - bx^-2)

dk/dx = 1/a (2x - b/x²)

Problem 3:

b = -3m^-8 + 3√7

Solution :

b = -3m^-8 + 3√7

db/dm = 24m^(-8-1) + 0

db/dm = 24m^-9

Problem 4 :

f = ax⁴ + bx² + c

Solution:

f = ax⁴ + bx² + c

df/dx = 4ax^(4-1) + 2bx^(2-1) + 0

df/dx = 4ax³ + 2bx

Problem 5:

r = t⁴/4 - t³/3 + t²/2 - t + 4

Solution:

r = t⁴/4 - t³/3 + t²/2 - t + 4

dr/dt = (4t³/4) - (3t²/3) + (2t/2) - 1 + 0

dr/dt = t³ - t² + t - 1

Problem 6:

g = -8h⁵ + 3h^-2 + h^1.6

Solution:

g = -8h⁵ + 3h^-2 + h^1.6

dg/dh = -40h^(5-1) - 6h^(-2-1) + 1.6h^(1.6-1))

= -40h⁴ - 6h^-3 + 1.6h^0.6

dg/dh = -40h⁴ - 6/h³ + 1.6h^0.6