What is (\partial)/(\partial x)(cos(x^2+xy)) ?

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

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(\partial)/(\partial x)(cos(x^2+xy))

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

- sin (x^{2} + x y) (2 x + y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= - sin (x^{2} + x y) (2 x + y)

x \to 5 + lim (\frac{x ^{2} + 2}{5 - x})

n = 3 \sum \infty \frac{6}{n ^{2} - 1}

x^{5} + y^{5} = 10

x \to 0 - lim (\frac{1}{13 x})

f (x) = \frac{4 ( x ^{2} - 1 )}{( 4 x ^{3} - 2 x ) ^{\frac{2}{3}}}

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