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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

x \to 2 + lim (3 + ∣ 2 x - 4 ∣)

\frac{d}{d y} (cos (x) - y)

(cot (y) + x^{2}) d x = x csc^{2} (y) d y

\frac{1}{x - 2}

9 e^{3 x}

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