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Calculus Help! How to find the derivative?

+1 vote
Calculate the derivative for
f(x) = x^3/2(2x^4 − 5x + x^−1/2)
asked Feb 25, 2013 in CALCULUS by linda Scholar

1 Answer

+2 votes

f(x) = [x3/2][2x4 - 5x + x-1/2]

f(x) = [x3/2][2x4 - 5x + 1/√x]

f(x) = [x3/2][2x4] - [x3/2][5x] + [x3/2][x-1/2]

Exponent Laws: xmxn = xm+n

f(x) = [x7] - (5/2)x4 + [x3/2][x-1/2]

f(x) = [x7] - (5/2)x4 + (1/2)[x5/2]

Apply 'derivative with respect to x' each side.

f'(x) = (d/dx){[x7] - (5/2)x4 + (1/2)[x5/2]}

f'(x) = (d/dx)[x7] - (d/dx)(5/2)x4 + (d/dx)(1/2)x5/2

Power Rule of Derivative (d/dx)xn = nxn-1

f'(x) = 7x6 - (5/2)(4x3) + (1/2)(5/2)[x3/2]

f'(x) = 7x6 - (5)(2x3) + (5/4)[x3/2]

f'(x) = 7x6 - 10x3 + (5/4)x3/2

Therefore the derivative of f(x) is 7x6 - 10x3 + (5/4)x3/2.

answered Feb 25, 2013 by britally Apprentice

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