What is (\partial)/(\partial x)(5sqrt(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(5sqrt(x^2+y^2)) is (5x)/(sqrt(x^2+y^2))

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(\partial)/(\partial x)(5sqrt(x^2+y^2))

\frac{\partial}{\partial x} (5 x^{2} + y^{2})

\frac{5 x}{x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (5 x^{2} + y^{2})

Treat

y

as a constant

Take the constant out:

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

= 5 \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

= 5 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x

Simplify

5 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x : \frac{5 x}{x ^{2} + y ^{2}}

= \frac{5 x}{x ^{2} + y ^{2}}

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (5) = 5

\frac{d}{d x} ((3 x - 2)^{5})

\int 4 e^{x} 8 + e^{x} d x

x \to 6 lim (x + 3)

(arctan (e^{x}))^{^{'}}

What is (\partial)/(\partial x)(5sqrt(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(5sqrt(x^2+y^2)) is (5x)/(sqrt(x^2+y^2))