What is the derivative of picsc(pi+(x^6/3)) ?

The derivative of picsc(pi+(x^6/3)) is 2pix^5cot((x^6)/3)csc((x^6)/3)

What is the first derivative of picsc(pi+(x^6/3)) ?

The first derivative of picsc(pi+(x^6/3)) is 2pix^5cot((x^6)/3)csc((x^6)/3)

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\frac{d}{d x} (π csc (π + \frac{x ^{6}}{3}))

2 π x^{5} cot (\frac{x ^{6}}{3}) csc (\frac{x ^{6}}{3})

Solution steps

\frac{d}{d x} (π csc (π + \frac{x ^{6}}{3}))

Simplify

π csc (π + \frac{x ^{6}}{3}) : - π csc (\frac{x ^{6}}{3})

= \frac{d}{d x} (- π csc (\frac{x ^{6}}{3}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - π \frac{d}{d x} (csc (\frac{x ^{6}}{3}))

Apply the chain rule:

- cot (\frac{x ^{6}}{3}) csc (\frac{x ^{6}}{3}) \frac{d}{d x} (\frac{x ^{6}}{3})

= - cot (\frac{x ^{6}}{3}) csc (\frac{x ^{6}}{3}) \frac{d}{d x} (\frac{x ^{6}}{3})

\frac{d}{d x} (\frac{x ^{6}}{3}) = 2 x^{5}

= - π (- cot (\frac{x ^{6}}{3}) csc (\frac{x ^{6}}{3}) \cdot 2 x^{5})

Simplify

= 2 π x^{5} cot (\frac{x ^{6}}{3}) csc (\frac{x ^{6}}{3})

What is the derivative of picsc(pi+(x^6/3)) ?
The derivative of picsc(pi+(x^6/3)) is 2pix^5cot((x^6)/3)csc((x^6)/3)
What is the first derivative of picsc(pi+(x^6/3)) ?
The first derivative of picsc(pi+(x^6/3)) is 2pix^5cot((x^6)/3)csc((x^6)/3)