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

The answer to (\partial)/(\partial x)(2x^2e^y+cos(xy)) is 4e^yx-sin(xy)y

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

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

4 e^{y} x - sin (x y) y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{2} e^{y}) = 4 e^{y} x

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

= 4 e^{y} x - sin (x y) y

y = x^{2}, (0, 4)

\int 0.8 x d x

\frac{\partial}{\partial y} (x^{2} + (y - 1)^{2} + z^{2})

x \to 4 lim (\frac{∣ x + 4 ∣}{x + 4})

\int \frac{5 x ^{2} + 8 x + 5}{( x - 5 ) ( x ^{2} + 9 )} d x

What is (\partial)/(\partial x)(2x^2e^y+cos(xy)) ?
The answer to (\partial)/(\partial x)(2x^2e^y+cos(xy)) is 4e^yx-sin(xy)y