# 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 + h1.6

Solution:

g = -8h5 + 3h-2 + h1.6

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

= -40h4 - 6h-3 + 1.6h0.6

dg/dh = -40h4 - 6/h3 + 1.6h0.6

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