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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{x}^{3} sin (t^{2}) d t

\frac{d}{d x} (\frac{50}{x ^{7}})

\frac{d y}{d x} (x 16 - x) = 0

4 e^{- 7 t} cos (9 t)

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