Find the derivatives of (a+x^3/4)(a-x1/4)

1.	Find the derivatives of (a+x^3/4)(a-x1/4)
Answer» f(x) = (a+x^3/4) (a-x^1/4) f'(x) = (a+x^3/4) d/dx (a-x^1/4) + (d/dx(a+x^3/4)) (a-x^1/4) = (a+x^3/4) x -1/4 x^-3/4 + 3/4 x^-1/4 (a-x^1/4) = -a/4 x^-3/4 - 1/4 + 3a/4 x^-1/4 - 3/4 = a/4 x^-1/4 (-x^-1/2 + 3) - 1

Answer»

f(x) = (a+x^3/4) (a-x^1/4)

f'(x) = (a+x^3/4) d/dx (a-x^1/4) + (d/dx(a+x^3/4)) (a-x^1/4)

= (a+x^3/4) x -1/4 x^-3/4 + 3/4 x^-1/4 (a-x^1/4)

= -a/4 x^-3/4 - 1/4 + 3a/4 x^-1/4 - 3/4

= a/4 x^-1/4 (-x^-1/2 + 3) - 1

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