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

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

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

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

cos (x^{2} + x y) (2 x + y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (x^{2} + x y) (2 x + y)

\frac{d}{d x} (\frac{x cos ( x )}{1 + e ^{x}})

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

4 - x^{2}, x^{2} - 2 x

y^{^{''}} - 2 y^{^{'}} + y = t e^{t} + 4

y^{^{''}} + 36 y = sec^{2} (6 x)

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