Respuesta :

Answer:

Step-by-step explanation:

[tex]f(x)=(x^{\frac{1}{4}}+11)(7 x^{\frac{1}{2}}+3)\\f'(x)=(x^{\frac{1}{4}}+11)(7*\frac{1}{2}x^{-\frac{1}{2}})+\frac{1}{4} x^{-\frac{3}{4}}(7 x^{\frac{1}{2}}+3)[/tex]

Answer:

21/4 x^-1/4 + 77/2 x^-1/2 + 3/4 x^-3/4.

Step-by-step explanation:

Use the product rule;

d(uv) = udv/dx + v du/dx

u = x^1/4 + 11 and v = 7x^1/2+ 3.

f'(x) =  (x^1/4 + 11)(7/2x^-1/2 + (7 x^1/2+ 3)1/4x^-3/4.

= 7/2x^-1/4 + 77/2x^-1/2 + 7/4x^-1/4 + 3/4x^-3/4

= 21/4 x^-1/4 + 77/2 x^-1/2 + 3/4 x^-3/4.

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