What is the derivative of arccsc(7x^3+9) ?

The derivative of arccsc(7x^3+9) is -(21x^2)/((7x^3+9)sqrt(49x^6+126x^3+80))

What is the first derivative of arccsc(7x^3+9) ?

The first derivative of arccsc(7x^3+9) is -(21x^2)/((7x^3+9)sqrt(49x^6+126x^3+80))

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\frac{d}{d x} (arccsc (7 x^{3} + 9))

- \frac{21 x ^{2}}{( 7 x ^{3} + 9 ) 49 x ^{6} + 126 x ^{3} + 80}

Solution steps

\frac{d}{d x} (arccsc (7 x^{3} + 9))

Apply the chain rule:

- \frac{1}{( 7 x ^{3} + 9 ) ^{2} ( 7 x ^{3} + 9 ) ^{2} - 1} \frac{d}{d x} (7 x^{3} + 9)

= - \frac{1}{( 7 x ^{3} + 9 ) ^{2} ( 7 x ^{3} + 9 ) ^{2} - 1} \frac{d}{d x} (7 x^{3} + 9)

\frac{d}{d x} (7 x^{3} + 9) = 21 x^{2}

= - \frac{1}{( 7 x ^{3} + 9 ) ^{2} ( 7 x ^{3} + 9 ) ^{2} - 1} \cdot 21 x^{2}

Simplify

- \frac{1}{( 7 x ^{3} + 9 ) ^{2} ( 7 x ^{3} + 9 ) ^{2} - 1} \cdot 21 x^{2} : - \frac{21 x ^{2}}{( 7 x ^{3} + 9 ) 49 x ^{6} + 126 x ^{3} + 80}

= - \frac{21 x ^{2}}{( 7 x ^{3} + 9 ) 49 x ^{6} + 126 x ^{3} + 80}

\int 6 x - 1 d x

\int \frac{ln ( 7 x )}{x ^{9}} d x

ln (x x^{2} - 1)

(- 3, - 2), (1, - 5)

\int cos (x) (1 + 7 sin^{2} (x)) d x

What is the derivative of arccsc(7x^3+9) ?
The derivative of arccsc(7x^3+9) is -(21x^2)/((7x^3+9)sqrt(49x^6+126x^3+80))
What is the first derivative of arccsc(7x^3+9) ?
The first derivative of arccsc(7x^3+9) is -(21x^2)/((7x^3+9)sqrt(49x^6+126x^3+80))