What is the derivative of (x^6+2/(8x^2)) ?

The derivative of (x^6+2/(8x^2)) is (x^6-1)/(2x^3)

What is the first derivative of (x^6+2/(8x^2)) ?

The first derivative of (x^6+2/(8x^2)) is (x^6-1)/(2x^3)

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\frac{d}{d x} (\frac{x ^{6} + 2}{8 x ^{2}})

\frac{x ^{6} - 1}{2 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{6} + 2}{8 x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (\frac{x ^{6} + 2}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( x ^{6} + 2 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{6} + 2 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{6} + 2) = 6 x^{5}

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

= \frac{1}{8} \cdot \frac{6 x ^{5} x ^{2} - 2 x ( x ^{6} + 2 )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{8} \cdot \frac{6 x ^{5} x ^{2} - 2 x ( x ^{6} + 2 )}{( x ^{2} ) ^{2}} : \frac{x ^{6} - 1}{2 x ^{3}}

= \frac{x ^{6} - 1}{2 x ^{3}}

\frac{5 u ^{2}}{( u ^{2} + u ) ^{3}}

\frac{\partial}{\partial x} (a cos (k x))

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

ln (x e^{- 3 x})

f (x) = \frac{9}{x}

What is the derivative of (x^6+2/(8x^2)) ?
The derivative of (x^6+2/(8x^2)) is (x^6-1)/(2x^3)
What is the first derivative of (x^6+2/(8x^2)) ?
The first derivative of (x^6+2/(8x^2)) is (x^6-1)/(2x^3)