What is (\partial)/(\partial y)(sin(x^5-7y)) ?

The answer to (\partial)/(\partial y)(sin(x^5-7y)) is -7cos(x^5-7y)

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(\partial)/(\partial y)(sin(x^5-7y))

\frac{\partial}{\partial y} (sin (x^{5} - 7 y))

- 7 cos (x^{5} - 7 y)

Solution steps

\frac{\partial}{\partial y} (sin (x^{5} - 7 y))

Treat

x

as a constant

Apply the chain rule:

cos (x^{5} - 7 y) \frac{\partial}{\partial y} (x^{5} - 7 y)

= cos (x^{5} - 7 y) \frac{\partial}{\partial y} (x^{5} - 7 y)

\frac{\partial}{\partial y} (x^{5} - 7 y) = - 7

= cos (x^{5} - 7 y) (- 7)

Simplify

= - 7 cos (x^{5} - 7 y)

\frac{d y}{d x} = (\frac{4}{x ^{2} + 1}) (y + 1)

y^{^{''}} + 4 y = e^{x}

φ^{3} cos (φ^{5})

\int \frac{1}{x ^{2} x ^{2} - 1} d x

f (x) = cos (8 x^{2} - 16) sin (x^{2})

What is (\partial)/(\partial y)(sin(x^5-7y)) ?
The answer to (\partial)/(\partial y)(sin(x^5-7y)) is -7cos(x^5-7y)