What is (\partial)/(\partial x)(-2xsin(x^2+y^2)) ?

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

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(\partial)/(\partial x)(-2xsin(x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x^{2} + y^{2})

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

\frac{\partial}{\partial x} (x) = 1

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

= - 2 (1 \cdot sin (x^{2} + y^{2}) + cos (x^{2} + y^{2}) \cdot 2 xx)

Simplify

- 2 (1 \cdot sin (x^{2} + y^{2}) + cos (x^{2} + y^{2}) \cdot 2 xx) : - 2 (sin (x^{2} + y^{2}) + 2 x^{2} cos (x^{2} + y^{2}))

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

x \to 3 lim (e^{\frac{3}{3 - x}})

\int_{a}^{b} \frac{1}{b - a} x d x

\int (e^{x} - 2 x^{2}) d x

x y^{^{'}} = x^{2} + 3 y

\int (1 - 2 x)^{5} d x

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