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

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

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

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

2 x + cos (x y) y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (sin (x y)) = cos (x y) y

= 2 x + cos (x y) y

\frac{d}{d x} (a cos (b x))

\int 4 x - \frac{4}{x} d x

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

t \frac{d y}{d t} + 5 y = t

\int \frac{3 x - 1}{( 3 x ^{2} - 2 x + 1 ) ^{4}} d x

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