What is the derivative of f(x)=3x^2-4/x+4/(sqrt(x)) ?

The derivative of f(x)=3x^2-4/x+4/(sqrt(x)) is (4x^{3/2}-2x^2+6x^{9/2})/(x^{7/2)}

What is the first derivative of f(x)=3x^2-4/x+4/(sqrt(x)) ?

The first derivative of f(x)=3x^2-4/x+4/(sqrt(x)) is (4x^{3/2}-2x^2+6x^{9/2})/(x^{7/2)}

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derivative of

f (x) = 3 x^{2} - \frac{4}{x} + \frac{4}{x}

\frac{4 x ^{\frac{3}{2}} - 2 x ^{2} + 6 x ^{\frac{9}{2}}}{x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (3 x^{2} - \frac{4}{x} + \frac{4}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (\frac{4}{x}) = - \frac{2}{x ^{\frac{3}{2}}}

= 6 x - (- \frac{4}{x ^{2}}) - \frac{2}{x ^{\frac{3}{2}}}

Simplify

6 x - (- \frac{4}{x ^{2}}) - \frac{2}{x ^{\frac{3}{2}}} : \frac{4 x ^{\frac{3}{2}} - 2 x ^{2} + 6 x ^{\frac{9}{2}}}{x ^{\frac{7}{2}}}

= \frac{4 x ^{\frac{3}{2}} - 2 x ^{2} + 6 x ^{\frac{9}{2}}}{x ^{\frac{7}{2}}}

\frac{d y}{d x} = sec^{2} (x)

x \to \infty lim (3 x - x^{2})

8 y^{^{''}} + 6 y^{^{'}} - y = 11

h \to 0 lim (cos (\frac{π}{2}))

\int_{0}^{4} e^{x} d x

What is the derivative of f(x)=3x^2-4/x+4/(sqrt(x)) ?
The derivative of f(x)=3x^2-4/x+4/(sqrt(x)) is (4x^{3/2}-2x^2+6x^{9/2})/(x^{7/2)}
What is the first derivative of f(x)=3x^2-4/x+4/(sqrt(x)) ?
The first derivative of f(x)=3x^2-4/x+4/(sqrt(x)) is (4x^{3/2}-2x^2+6x^{9/2})/(x^{7/2)}