What is (\partial)/(\partial x)(3xsqrt(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(3xsqrt(x^2+y^2)) is (3(2x^2+y^2))/(sqrt(x^2+y^2))

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(\partial)/(\partial x)(3xsqrt(x^2+y^2))

\frac{\partial}{\partial x} (3 x x^{2} + y^{2})

\frac{3 ( 2 x ^{2} + y ^{2} )}{x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (3 x x^{2} + y^{2})

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (x x^{2} + y^{2})

Apply the Product Rule:

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

f = x, g = x^{2} + y^{2}

= 3 (\frac{\partial}{\partial x} (x) x^{2} + y^{2} + \frac{\partial}{\partial x} (x^{2} + y^{2}) x)

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

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

= 3 (1 \cdot x^{2} + y^{2} + \frac{x}{x ^{2} + y ^{2}} x)

Simplify

3 (1 \cdot x^{2} + y^{2} + \frac{x}{x ^{2} + y ^{2}} x) : \frac{3 ( 2 x ^{2} + y ^{2} )}{x ^{2} + y ^{2}}

= \frac{3 ( 2 x ^{2} + y ^{2} )}{x ^{2} + y ^{2}}

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

\int \frac{1}{x ^{2} 225 - x ^{2}} d x

\frac{d y}{d x} = sin (6 x)

y^{^{'}} = 3 - 2 y

\int 7 tan^{2} (x) d x

What is (\partial)/(\partial x)(3xsqrt(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(3xsqrt(x^2+y^2)) is (3(2x^2+y^2))/(sqrt(x^2+y^2))