What is the derivative of (((x^6)-1))/(((x^6)+1)) ?

The derivative of (((x^6)-1))/(((x^6)+1)) is (12x^5)/((x^6+1)^2)

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

The first derivative of (((x^6)-1))/(((x^6)+1)) is (12x^5)/((x^6+1)^2)

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derivative of

\frac{( ( x ^{6} ) - 1 )}{( ( x ^{6} ) + 1 )}

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

Solution steps

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

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

\frac{d}{d x} (x^{6} - 1) = 6 x^{5}

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

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

Expand

6 x^{5} (x^{6} + 1) - 6 x^{5} (x^{6} - 1) : 12 x^{5}

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

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

y = 3 cos (x) + 7 e x + ln (x^{2} + 1)

f (x) = \frac{4 x - 1}{x}

2^{z}

y = sin (x^{- 1})

What is the derivative of (((x^6)-1))/(((x^6)+1)) ?
The derivative of (((x^6)-1))/(((x^6)+1)) is (12x^5)/((x^6+1)^2)
What is the first derivative of (((x^6)-1))/(((x^6)+1)) ?
The first derivative of (((x^6)-1))/(((x^6)+1)) is (12x^5)/((x^6+1)^2)