What is the derivative of f(x)=arccsc(3x) ?

The derivative of f(x)=arccsc(3x) is -1/(sqrt(x^2)\sqrt{9x^2-1)}

What is the first derivative of f(x)=arccsc(3x) ?

The first derivative of f(x)=arccsc(3x) is -1/(sqrt(x^2)\sqrt{9x^2-1)}

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derivative of

f (x) = arccsc (3 x)

- \frac{1}{x ^{2} 9 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arccsc (3 x))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = 3

= - \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3

Simplify

- \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3 : - \frac{1}{x ^{2} 9 x ^{2} - 1}

= - \frac{1}{x ^{2} 9 x ^{2} - 1}

\frac{\partial}{\partial x} (sin (4 x^{3} y - 5 x y^{4}))

x \to 4 lim (7^{x} + 12 x)

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

y = 6^{x}

y = 7 x, (7, 7)

What is the derivative of f(x)=arccsc(3x) ?
The derivative of f(x)=arccsc(3x) is -1/(sqrt(x^2)\sqrt{9x^2-1)}
What is the first derivative of f(x)=arccsc(3x) ?
The first derivative of f(x)=arccsc(3x) is -1/(sqrt(x^2)\sqrt{9x^2-1)}