What is (\partial)/(\partial x)(sin^4(x-7y)) ?

The answer to (\partial)/(\partial x)(sin^4(x-7y)) is 4sin^3(x-7y)cos(x-7y)

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(\partial)/(\partial x)(sin^4(x-7y))

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

4 sin^{3} (x - 7 y) cos (x - 7 y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

4 (sin (x - 7 y))^{3} \frac{\partial}{\partial x} (sin (x - 7 y))

= 4 (sin (x - 7 y))^{3} \frac{\partial}{\partial x} (sin (x - 7 y))

\frac{\partial}{\partial x} (sin (x - 7 y)) = cos (x - 7 y)

= 4 (sin (x - 7 y))^{3} cos (x - 7 y)

Simplify

= 4 sin^{3} (x - 7 y) cos (x - 7 y)

\int 5 x d x

\int 1 + \frac{( x - 1 ) ^{2}}{4 x} d x

x \to - \infty lim (2 e^{x})

\frac{d}{d x} (A x + B)

4 d y + y d x = x^{2} d y

What is (\partial)/(\partial x)(sin^4(x-7y)) ?
The answer to (\partial)/(\partial x)(sin^4(x-7y)) is 4sin^3(x-7y)cos(x-7y)