What is the derivative of sin^6(pix) ?

The derivative of sin^6(pix) is 6pisin^5(pix)cos(pix)

What is the first derivative of sin^6(pix) ?

The first derivative of sin^6(pix) is 6pisin^5(pix)cos(pix)

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\frac{d}{d x} (sin^{6} (π x))

6 π sin^{5} (π x) cos (π x)

Solution steps

\frac{d}{d x} (sin^{6} (π x))

Apply the chain rule:

6 (sin (π x))^{5} \frac{d}{d x} (sin (π x))

= 6 (sin (π x))^{5} \frac{d}{d x} (sin (π x))

\frac{d}{d x} (sin (π x)) = cos (π x) π

= 6 (sin (π x))^{5} cos (π x) π

Simplify

= 6 π sin^{5} (π x) cos (π x)

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

\int \frac{7 x ^{3}}{7 + x ^{2}} d x

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

\frac{d}{d x} (\frac{x}{1 + 5 x ^{2}})

(t - 1)^{2} y^{^{'}} + 3 (t - 1) y = t + 2

What is the derivative of sin^6(pix) ?
The derivative of sin^6(pix) is 6pisin^5(pix)cos(pix)
What is the first derivative of sin^6(pix) ?
The first derivative of sin^6(pix) is 6pisin^5(pix)cos(pix)