What is (\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11) ?

The answer to (\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11) is 2xy^3+2/(y^3)+5

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(\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11)

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x y^{- 3} + 5 x + 3 y + 11)

2 x y^{3} + \frac{2}{y ^{3}} + 5

Solution steps

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x y^{- 3} + 5 x + 3 y + 11)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2} y^{3}) + \frac{\partial}{\partial x} (2 x y^{- 3}) + \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (3 y) + \frac{\partial}{\partial x} (11)

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

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

\frac{\partial}{\partial x} (5 x) = 5

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (11) = 0

= 2 y^{3} x + \frac{2}{y ^{3}} + 5 + 0 + 0

Simplify

= 2 x y^{3} + \frac{2}{y ^{3}} + 5

t \to 5 lim (\frac{1}{t ^{2} - 4 t - 5} - \frac{1}{6 ( t - 5 )})

cos (x) sin (x)

\int \frac{1}{2} sin (2 t) d t

n = 0 \sum \infty \frac{x ^{n}}{n + 2}

x \to 0 lim (\frac{8}{1 + sin ( x )})

What is (\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11) ?
The answer to (\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11) is 2xy^3+2/(y^3)+5