What is the derivative of sin((pix^5)) ?

The derivative of sin((pix^5)) is cos(pi^5x^5)*5pi^5x^4

What is the first derivative of sin((pix^5)) ?

The first derivative of sin((pix^5)) is cos(pi^5x^5)*5pi^5x^4

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\frac{d}{d x} (sin ((π x)^{5}))

cos (π^{5} x^{5}) \cdot 5 π^{5} x^{4}

Solution steps

\frac{d}{d x} (sin ((π x)^{5}))

Simplify

sin ((π x)^{5}) : sin (π^{5} x^{5})

= \frac{d}{d x} (sin (π^{5} x^{5}))

Apply the chain rule:

cos (π^{5} x^{5}) \frac{d}{d x} (π^{5} x^{5})

= cos (π^{5} x^{5}) \frac{d}{d x} (π^{5} x^{5})

\frac{d}{d x} (π^{5} x^{5}) = 5 π^{5} x^{4}

= cos (π^{5} x^{5}) \cdot 5 π^{5} x^{4}

(7.3) (6.7)

f (x) = \frac{10 x}{x + 4}, at x = 4, y = 5

\frac{d}{d x} (4 x^{4} y^{3} + cos (x^{2}))

\int x^{2 n} d x

\frac{d}{d x} (\frac{x ^{4}}{8})

What is the derivative of sin((pix^5)) ?
The derivative of sin((pix^5)) is cos(pi^5x^5)*5pi^5x^4
What is the first derivative of sin((pix^5)) ?
The first derivative of sin((pix^5)) is cos(pi^5x^5)*5pi^5x^4