What is the derivative of ((x^3-1/(x^3+1))^7) ?

The derivative of ((x^3-1/(x^3+1))^7) is (42x^2(x^3-1)^6)/((x^3+1)^8)

What is the first derivative of ((x^3-1/(x^3+1))^7) ?

The first derivative of ((x^3-1/(x^3+1))^7) is (42x^2(x^3-1)^6)/((x^3+1)^8)

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\frac{d}{d x} ((\frac{x ^{3} - 1}{x ^{3} + 1})^{7})

\frac{42 x ^{2} ( x ^{3} - 1 ) ^{6}}{( x ^{3} + 1 ) ^{8}}

Solution steps

\frac{d}{d x} ((\frac{x ^{3} - 1}{x ^{3} + 1})^{7})

Apply the chain rule:

7 (\frac{x ^{3} - 1}{x ^{3} + 1})^{6} \frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

= 7 (\frac{x ^{3} - 1}{x ^{3} + 1})^{6} \frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1}) = \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

= 7 (\frac{x ^{3} - 1}{x ^{3} + 1})^{6} \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

Simplify

7 (\frac{x ^{3} - 1}{x ^{3} + 1})^{6} \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}} : \frac{42 x ^{2} ( x ^{3} - 1 ) ^{6}}{( x ^{3} + 1 ) ^{8}}

= \frac{42 x ^{2} ( x ^{3} - 1 ) ^{6}}{( x ^{3} + 1 ) ^{8}}

arctan (x + y) = y^{2} + \frac{π}{4}, (1, 0)

\int (x^{3} + 5 x^{2} - 2) e^{2 x} d x

y^{^{'}} = x^{2} - y - 2

\int (x - 1) (x^{2} - 2 x + 5)^{6} d x

f (x) = 7 - x

What is the derivative of ((x^3-1/(x^3+1))^7) ?
The derivative of ((x^3-1/(x^3+1))^7) is (42x^2(x^3-1)^6)/((x^3+1)^8)
What is the first derivative of ((x^3-1/(x^3+1))^7) ?
The first derivative of ((x^3-1/(x^3+1))^7) is (42x^2(x^3-1)^6)/((x^3+1)^8)