What is the derivative of (x^6/(sqrt(1+x^{12))}) ?

The derivative of (x^6/(sqrt(1+x^{12))}) is (6x^5)/((1+x^{12))sqrt(1+x^{12)}}

What is the first derivative of (x^6/(sqrt(1+x^{12))}) ?

The first derivative of (x^6/(sqrt(1+x^{12))}) is (6x^5)/((1+x^{12))sqrt(1+x^{12)}}

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\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

\frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

Solution steps

\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{6} ) 1 + x ^{12} - \frac{d}{d x} ( 1 + x ^{12} ) x ^{6}}{( 1 + x ^{12} ) ^{2}}

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

\frac{d}{d x} (1 + x^{12}) = \frac{6 x ^{11}}{1 + x ^{12}}

= \frac{6 x ^{5} 1 + x ^{12} - \frac{6 x ^{11}}{1 + x ^{12}} x ^{6}}{( 1 + x ^{12} ) ^{2}}

Simplify

\frac{6 x ^{5} 1 + x ^{12} - \frac{6 x ^{11}}{1 + x ^{12}} x ^{6}}{( 1 + x ^{12} ) ^{2}} : \frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

= \frac{6 x ^{5}}{( 1 + x ^{12} ) 1 + x ^{12}}

What is the derivative of (x^6/(sqrt(1+x^{12))}) ?
The derivative of (x^6/(sqrt(1+x^{12))}) is (6x^5)/((1+x^{12))sqrt(1+x^{12)}}
What is the first derivative of (x^6/(sqrt(1+x^{12))}) ?
The first derivative of (x^6/(sqrt(1+x^{12))}) is (6x^5)/((1+x^{12))sqrt(1+x^{12)}}