What is (\partial)/(\partial x)(sin(x^2-5xy)) ?

The answer to (\partial)/(\partial x)(sin(x^2-5xy)) is cos(x^2-5xy)(2x-5y)

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(\partial)/(\partial x)(sin(x^2-5xy))

\frac{\partial}{\partial x} (sin (x^{2} - 5 x y))

cos (x^{2} - 5 x y) (2 x - 5 y)

Solution steps

\frac{\partial}{\partial x} (sin (x^{2} - 5 x y))

Treat

y

as a constant

Apply the chain rule:

cos (x^{2} - 5 x y) \frac{\partial}{\partial x} (x^{2} - 5 x y)

= cos (x^{2} - 5 x y) \frac{\partial}{\partial x} (x^{2} - 5 x y)

\frac{\partial}{\partial x} (x^{2} - 5 x y) = 2 x - 5 y

= cos (x^{2} - 5 x y) (2 x - 5 y)

\int \frac{1}{3 x} d x

\frac{d}{d x} ((e^{(x^{2})} + 4)^{2} (4 x)^{3} x)

\int \frac{1}{sin ( x ) cos ^{3} ( x )} d x

\int_{3}^{4} \frac{( 2 x - 3 )}{6} d x

1 - 9 x^{2} y^{^{'}} = x

What is (\partial)/(\partial x)(sin(x^2-5xy)) ?
The answer to (\partial)/(\partial x)(sin(x^2-5xy)) is cos(x^2-5xy)(2x-5y)