What is (\partial)/(\partial x)(sin^6(3x-4y)) ?

The answer to (\partial)/(\partial x)(sin^6(3x-4y)) is 18sin^5(3x-4y)cos(3x-4y)

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(\partial)/(\partial x)(sin^6(3x-4y))

\frac{\partial}{\partial x} (sin^{6} (3 x - 4 y))

18 sin^{5} (3 x - 4 y) cos (3 x - 4 y)

Solution steps

\frac{\partial}{\partial x} (sin^{6} (3 x - 4 y))

Treat

y

as a constant

Apply the chain rule:

6 (sin (3 x - 4 y))^{5} \frac{\partial}{\partial x} (sin (3 x - 4 y))

= 6 (sin (3 x - 4 y))^{5} \frac{\partial}{\partial x} (sin (3 x - 4 y))

\frac{\partial}{\partial x} (sin (3 x - 4 y)) = cos (3 x - 4 y) \cdot 3

= 6 (sin (3 x - 4 y))^{5} cos (3 x - 4 y) \cdot 3

Simplify

= 18 sin^{5} (3 x - 4 y) cos (3 x - 4 y)

\frac{d}{d y} ((4 - y)^{\frac{1}{3}})

x \to 0 lim (3 x + 5)

y^{^{'}} - \frac{6}{x} y = \frac{y ^{5}}{x ^{20}}, y (1) = 1

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\int cos^{4} (7 x) d x

What is (\partial)/(\partial x)(sin^6(3x-4y)) ?
The answer to (\partial)/(\partial x)(sin^6(3x-4y)) is 18sin^5(3x-4y)cos(3x-4y)