What is the derivative of (x^2)/((1+x^{18))} ?

The derivative of (x^2)/((1+x^{18))} is (2x-16x^{19})/((1+x^{18))^2}

What is the first derivative of (x^2)/((1+x^{18))} ?

The first derivative of (x^2)/((1+x^{18))} is (2x-16x^{19})/((1+x^{18))^2}

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derivative of

\frac{x ^{2}}{( 1 + x ^{18} )}

\frac{2 x - 16 x ^{19}}{( 1 + x ^{18} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{18}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + x ^{18} ) - \frac{d}{d x} ( 1 + x ^{18} ) x ^{2}}{( 1 + x ^{18} ) ^{2}}

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

\frac{d}{d x} (1 + x^{18}) = 18 x^{17}

= \frac{2 x ( 1 + x ^{18} ) - 18 x ^{17} x ^{2}}{( 1 + x ^{18} ) ^{2}}

Simplify

\frac{2 x ( 1 + x ^{18} ) - 18 x ^{17} x ^{2}}{( 1 + x ^{18} ) ^{2}} : \frac{2 x - 16 x ^{19}}{( 1 + x ^{18} ) ^{2}}

= \frac{2 x - 16 x ^{19}}{( 1 + x ^{18} ) ^{2}}

What is the derivative of (x^2)/((1+x^{18))} ?
The derivative of (x^2)/((1+x^{18))} is (2x-16x^{19})/((1+x^{18))^2}
What is the first derivative of (x^2)/((1+x^{18))} ?
The first derivative of (x^2)/((1+x^{18))} is (2x-16x^{19})/((1+x^{18))^2}