What is the derivative of (x+csc(x^3+3)^{-3}) ?

The derivative of (x+csc(x^3+3)^{-3}) is -(3(1-3x^2cot(x^3+3)csc(x^3+3)))/((x+csc(x^3+3))^4)

What is the first derivative of (x+csc(x^3+3)^{-3}) ?

The first derivative of (x+csc(x^3+3)^{-3}) is -(3(1-3x^2cot(x^3+3)csc(x^3+3)))/((x+csc(x^3+3))^4)

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

- \frac{3 ( 1 - 3 x ^{2} cot ( x ^{3} + 3 ) csc ( x ^{3} + 3 ) )}{( x + csc ( x ^{3} + 3 ) ) ^{4}}

Solution steps

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

Apply the chain rule:

- \frac{3}{( x + csc ( x ^{3} + 3 ) ) ^{4}} \frac{d}{d x} (x + csc (x^{3} + 3))

= - \frac{3}{( x + csc ( x ^{3} + 3 ) ) ^{4}} \frac{d}{d x} (x + csc (x^{3} + 3))

\frac{d}{d x} (x + csc (x^{3} + 3)) = 1 - cot (x^{3} + 3) csc (x^{3} + 3) \cdot 3 x^{2}

= - \frac{3}{( x + csc ( x ^{3} + 3 ) ) ^{4}} (1 - cot (x^{3} + 3) csc (x^{3} + 3) \cdot 3 x^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 ( 1 - 3 x ^{2} cot ( x ^{3} + 3 ) csc ( x ^{3} + 3 ) )}{( x + csc ( x ^{3} + 3 ) ) ^{4}}

y = \frac{e ^{x}}{8 x ^{4}}

n \to \infty lim (\frac{n ^{2}}{2 n - 1} sin (\frac{1}{n}))

\frac{d}{d x} (ln (x^{2} + 5))

\frac{d}{d x} ((5 + 3 x) sin (x))

(y^{4} x) (\frac{d y}{d x}) = 1 + x, y (1) = 15

What is the derivative of (x+csc(x^3+3)^{-3}) ?
The derivative of (x+csc(x^3+3)^{-3}) is -(3(1-3x^2cot(x^3+3)csc(x^3+3)))/((x+csc(x^3+3))^4)
What is the first derivative of (x+csc(x^3+3)^{-3}) ?
The first derivative of (x+csc(x^3+3)^{-3}) is -(3(1-3x^2cot(x^3+3)csc(x^3+3)))/((x+csc(x^3+3))^4)