What is (\partial)/(\partial x)(sin^8(x-4y)) ?

The answer to (\partial)/(\partial x)(sin^8(x-4y)) is 8sin^7(x-4y)cos(x-4y)

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(\partial)/(\partial x)(sin^8(x-4y))

\frac{\partial}{\partial x} (sin^{8} (x - 4 y))

8 sin^{7} (x - 4 y) cos (x - 4 y)

Solution steps

\frac{\partial}{\partial x} (sin^{8} (x - 4 y))

Treat

y

as a constant

Apply the chain rule:

8 (sin (x - 4 y))^{7} \frac{\partial}{\partial x} (sin (x - 4 y))

= 8 (sin (x - 4 y))^{7} \frac{\partial}{\partial x} (sin (x - 4 y))

\frac{\partial}{\partial x} (sin (x - 4 y)) = cos (x - 4 y)

= 8 (sin (x - 4 y))^{7} cos (x - 4 y)

Simplify

= 8 sin^{7} (x - 4 y) cos (x - 4 y)

x \to 1 lim (\frac{10 x - 9 - 1}{x - 1})

\frac{d}{d x} (ln (3 x + 4))

ln (t^{2} + 6)

t^{2} e^{t}

\frac{\partial}{\partial x} (sin (4 y) e^{- 5 x})

What is (\partial)/(\partial x)(sin^8(x-4y)) ?
The answer to (\partial)/(\partial x)(sin^8(x-4y)) is 8sin^7(x-4y)cos(x-4y)