What is the derivative of csc((3x^4/(5x))) ?

The derivative of csc((3x^4/(5x))) is -(9x^2cot((3x^3)/5)csc((3x^3)/5))/(5)

What is the first derivative of csc((3x^4/(5x))) ?

The first derivative of csc((3x^4/(5x))) is -(9x^2cot((3x^3)/5)csc((3x^3)/5))/(5)

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\frac{d}{d x} (csc (\frac{3 x ^{4}}{5 x}))

- \frac{9 x ^{2} cot ( \frac{3 x ^{3}}{5} ) csc ( \frac{3 x ^{3}}{5} )}{5}

Solution steps

\frac{d}{d x} (csc (\frac{3 x ^{4}}{5 x}))

Simplify

csc (\frac{3 x ^{4}}{5 x}) : csc (\frac{3 x ^{3}}{5})

= \frac{d}{d x} (csc (\frac{3 x ^{3}}{5}))

Apply the chain rule:

- cot (\frac{3 x ^{3}}{5}) csc (\frac{3 x ^{3}}{5}) \frac{d}{d x} (\frac{3 x ^{3}}{5})

= - cot (\frac{3 x ^{3}}{5}) csc (\frac{3 x ^{3}}{5}) \frac{d}{d x} (\frac{3 x ^{3}}{5})

\frac{d}{d x} (\frac{3 x ^{3}}{5}) = \frac{9 x ^{2}}{5}

= - cot (\frac{3 x ^{3}}{5}) csc (\frac{3 x ^{3}}{5}) \frac{9 x ^{2}}{5}

Multiply fractions:

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

= - \frac{9 x ^{2} cot ( \frac{3 x ^{3}}{5} ) csc ( \frac{3 x ^{3}}{5} )}{5}

\int_{0}^{\frac{π}{8}} 3 cos^{5} (4 x) d x

\int \frac{x ^{2} - 2 x + 1}{x ^{2} - 2 x + 37} d x

n = 0 \sum \infty \frac{x ^{2 n}}{2 n !}

\int 2 + 60 x - 5 x^{2} d x

e^{- 5 s} \frac{1}{1 + s}

What is the derivative of csc((3x^4/(5x))) ?
The derivative of csc((3x^4/(5x))) is -(9x^2cot((3x^3)/5)csc((3x^3)/5))/(5)
What is the first derivative of csc((3x^4/(5x))) ?
The first derivative of csc((3x^4/(5x))) is -(9x^2cot((3x^3)/5)csc((3x^3)/5))/(5)