What is the derivative of ((x^7)/(sqrt(x^{14)+1)}) ?

The derivative of ((x^7)/(sqrt(x^{14)+1)}) is (7x^6)/((x^{14)+1)sqrt(x^{14)+1}}

What is the first derivative of ((x^7)/(sqrt(x^{14)+1)}) ?

The first derivative of ((x^7)/(sqrt(x^{14)+1)}) is (7x^6)/((x^{14)+1)sqrt(x^{14)+1}}

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\frac{d}{d x} (\frac{( x ^{7} )}{x ^{14} + 1})

\frac{7 x ^{6}}{( x ^{14} + 1 ) x ^{14} + 1}

Solution steps

\frac{d}{d x} (\frac{( x ^{7} )}{x ^{14} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{7} ) x ^{14} + 1 - \frac{d}{d x} ( x ^{14} + 1 ) x ^{7}}{( x ^{14} + 1 ) ^{2}}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (x^{14} + 1) = \frac{7 x ^{13}}{x ^{14} + 1}

= \frac{7 x ^{6} x ^{14} + 1 - \frac{7 x ^{13}}{x ^{14} + 1} x ^{7}}{( x ^{14} + 1 ) ^{2}}

Simplify

\frac{7 x ^{6} x ^{14} + 1 - \frac{7 x ^{13}}{x ^{14} + 1} x ^{7}}{( x ^{14} + 1 ) ^{2}} : \frac{7 x ^{6}}{( x ^{14} + 1 ) x ^{14} + 1}

= \frac{7 x ^{6}}{( x ^{14} + 1 ) x ^{14} + 1}

\int ln (x^{2} + a^{2}) d x

\frac{\partial}{\partial x} (x + i y)

\int \frac{( x - 1 )}{x ^{3} - x ^{2} - 2 x} d x

2 - x

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

What is the derivative of ((x^7)/(sqrt(x^{14)+1)}) ?
The derivative of ((x^7)/(sqrt(x^{14)+1)}) is (7x^6)/((x^{14)+1)sqrt(x^{14)+1}}
What is the first derivative of ((x^7)/(sqrt(x^{14)+1)}) ?
The first derivative of ((x^7)/(sqrt(x^{14)+1)}) is (7x^6)/((x^{14)+1)sqrt(x^{14)+1}}