What is (\partial)/(\partial x)(sin(x^2-9xy)) ?

The answer to (\partial)/(\partial x)(sin(x^2-9xy)) is cos(x^2-9xy)(2x-9y)

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(\partial)/(\partial x)(sin(x^2-9xy))

\frac{\partial}{\partial x} (sin (x^{2} - 9 x y))

cos (x^{2} - 9 x y) (2 x - 9 y)

Solution steps

\frac{\partial}{\partial x} (sin (x^{2} - 9 x y))

Treat

y

as a constant

Apply the chain rule:

cos (x^{2} - 9 x y) \frac{\partial}{\partial x} (x^{2} - 9 x y)

= cos (x^{2} - 9 x y) \frac{\partial}{\partial x} (x^{2} - 9 x y)

\frac{\partial}{\partial x} (x^{2} - 9 x y) = 2 x - 9 y

= cos (x^{2} - 9 x y) (2 x - 9 y)

\int \frac{1}{cos ^{5} ( x )} d x

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 6

\frac{2}{x ^{\frac{1}{3}}} - 2

2 y^{^{'}} + t y = 7

\frac{d}{d x} (\frac{3 x - 1}{2 x + 5})

What is (\partial)/(\partial x)(sin(x^2-9xy)) ?
The answer to (\partial)/(\partial x)(sin(x^2-9xy)) is cos(x^2-9xy)(2x-9y)