What is (\partial)/(\partial x)(sin(x^1y^3)) ?

The answer to (\partial)/(\partial x)(sin(x^1y^3)) is cos(xy^3)y^3

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(\partial)/(\partial x)(sin(x^1y^3))

\frac{\partial}{\partial x} (sin (x^{1} y^{3}))

cos (x y^{3}) y^{3}

Solution steps

\frac{\partial}{\partial x} (sin (x^{1} y^{3}))

Simplify

sin (x^{1} y^{3}) : sin (x y^{3})

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

Treat

y

as a constant

Apply the chain rule:

cos (x y^{3}) \frac{\partial}{\partial x} (x y^{3})

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

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

= cos (x y^{3}) y^{3}

(- 2 cos (2 x) - sin (3 x))^{2}

x \to \frac{1}{2} lim (arcsin (x))

f (x) = x^{2} + x - 3

3 t^{4} y^{^{''}} + 7 t^{3} y^{^{'}} = 0

n = 0 \sum \infty \frac{1}{( n + 10 )}

What is (\partial)/(\partial x)(sin(x^1y^3)) ?
The answer to (\partial)/(\partial x)(sin(x^1y^3)) is cos(xy^3)y^3