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

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

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(\partial)/(\partial x)(cos(x^2+y^2)*2x)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int_{0}^{π} cos^{4} (2 t) d t

\frac{d}{d x} ((x^{3} - x)^{3})

x^{2} y^{^{'}} + 2 x y = sin (3 x)

x \to 0 - lim (\frac{x + 94}{x})

\frac{d}{d t} (\frac{2 t}{t ^{2} + 1})

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