What is the derivative of 1/4 x^4+1/(8x^2) ?

The derivative of 1/4 x^4+1/(8x^2) is x^3-1/(4x^3)

What is the first derivative of 1/4 x^4+1/(8x^2) ?

The first derivative of 1/4 x^4+1/(8x^2) is x^3-1/(4x^3)

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\frac{d}{d x} (\frac{1}{4} x^{4} + \frac{1}{8 x ^{2}})

x^{3} - \frac{1}{4 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{1}{4} x^{4} + \frac{1}{8 x ^{2}})

Simplify

\frac{1}{4} x^{4} + \frac{1}{8 x ^{2}} : \frac{x ^{4}}{4} + \frac{1}{8 x ^{2}}

= \frac{d}{d x} (\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4}}{4}) + \frac{d}{d x} (\frac{1}{8 x ^{2}})

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

\frac{d}{d x} (\frac{1}{8 x ^{2}}) = - \frac{1}{4 x ^{3}}

= x^{3} - \frac{1}{4 x ^{3}}

\frac{d}{d x} (\frac{3}{x + 6})

\int e^{x} x - e^{x} + C d x

\frac{d}{d y} (y x)

x, x^{\frac{1}{2}}, 0, 2

\int (sec (2 x) tan (2 x) - \frac{4}{x ^{2}}) d x

What is the derivative of 1/4 x^4+1/(8x^2) ?
The derivative of 1/4 x^4+1/(8x^2) is x^3-1/(4x^3)
What is the first derivative of 1/4 x^4+1/(8x^2) ?
The first derivative of 1/4 x^4+1/(8x^2) is x^3-1/(4x^3)