What is (\partial)/(\partial x)(15sqrt(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(15sqrt(x^2+y^2)) is (15x)/(sqrt(x^2+y^2))

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(\partial)/(\partial x)(15sqrt(x^2+y^2))

\frac{\partial}{\partial x} (15 x^{2} + y^{2})

\frac{15 x}{x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (15 x^{2} + y^{2})

Treat

y

as a constant

Take the constant out:

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

= 15 \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

= 15 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x

Simplify

15 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x : \frac{15 x}{x ^{2} + y ^{2}}

= \frac{15 x}{x ^{2} + y ^{2}}

\int 2 y (- y + 2) d y

\frac{d}{d x} (ln (x + 1) - x + 1)

x \to 5 lim (4 x^{2} - 8)

\frac{d}{d x} (x x + 9)

What is (\partial)/(\partial x)(15sqrt(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(15sqrt(x^2+y^2)) is (15x)/(sqrt(x^2+y^2))