If f(x)=x^{5/2}+x³/2}+x¹/2}-7 then f'(x) is

\;5/2 x³/2} + \;3/2 x¹/2} - \;1/2 x^{-1/2}

\;5/2 x³/2} + \;3/2 x¹/2} + \;1/2 x^{-1/2} - 7

\;5/2 x³/2} + \;3/2 x¹/2} + \;1/2 x^{-1/2}

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Differential Calculus

Question : 1 of 69

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f(x)=x^{\frac{5}{2}}+x^{\frac{3}{2}}+x^{\frac{1}{2}}-7

f'(x)

$\;\frac{5}{2} x^{\frac{3}{2}} + \;\frac{3}{2} x^{\frac{1}{2}} - \;\frac{1}{2} x^{-\frac{1}{2}}$
$\;\frac{5}{2} x^{\frac{3}{2}} + \;\frac{3}{2} x^{\frac{1}{2}} + \;\frac{1}{2} x^{-\frac{1}{2}} - 7$
$\;\frac{5}{2} x^{\frac{3}{2}} + \;\frac{3}{2} x^{\frac{1}{2}} + \;\frac{1}{2} x^{-\frac{1}{2}}$
none

Solution:

Concept:

Differentiate each term using the power rule: if

f(x) = x^n

, then

f'(x) = nx^{n-1}

Explanation:

Given

f(x) = x^{\frac{5}{2}} + x^{\frac{3}{2}} + x^{\frac{1}{2}} - 7

Differentiate term by term:

•

\frac{d}{dx} x^{\frac{5}{2}} = \frac{5}{2} x^{\frac{3}{2}}

•

\frac{d}{dx} x^{\frac{3}{2}} = \frac{3}{2} x^{\frac{1}{2}}

•

\frac{d}{dx} x^{\frac{1}{2}} = \frac{1}{2} x^{-\frac{1}{2}}

•

\frac{d}{dx}(-7) = 0

Thus

f'(x) = \frac{5}{2} x^{\frac{3}{2}} + \frac{3}{2} x^{\frac{1}{2}} + \frac{1}{2} x^{-\frac{1}{2}}

Answer:

Option C:

\frac{5}{2} x^{\frac{3}{2}} + \frac{3}{2} x^{\frac{1}{2}} + \frac{1}{2} x^{-\frac{1}{2}}

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