What is (\partial)/(\partial x)((10-x^3-y^2)/(12x)) ?

The answer to (\partial)/(\partial x)((10-x^3-y^2)/(12x)) is (-2x^3+y^2-10)/(12x^2)

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(\partial)/(\partial x)((10-x^3-y^2)/(12x))

\frac{\partial}{\partial x} (\frac{10 - x ^{3} - y ^{2}}{12 x})

\frac{- 2 x ^{3} + y ^{2} - 10}{12 x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{10 - x ^{3} - y ^{2}}{12 x})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{12} \frac{\partial}{\partial x} (\frac{10 - x ^{3} - y ^{2}}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{12} \cdot \frac{\frac{\partial}{\partial x} ( 10 - x ^{3} - y ^{2} ) x - \frac{\partial}{\partial x} ( x ) ( 10 - x ^{3} - y ^{2} )}{x ^{2}}

\frac{\partial}{\partial x} (10 - x^{3} - y^{2}) = - 3 x^{2}

\frac{\partial}{\partial x} (x) = 1

= \frac{1}{12} \cdot \frac{( - 3 x ^{2} ) x - 1 \cdot ( 10 - x ^{3} - y ^{2} )}{x ^{2}}

Simplify

\frac{1}{12} \cdot \frac{( - 3 x ^{2} ) x - 1 \cdot ( 10 - x ^{3} - y ^{2} )}{x ^{2}} : \frac{- 2 x ^{3} + y ^{2} - 10}{12 x ^{2}}

= \frac{- 2 x ^{3} + y ^{2} - 10}{12 x ^{2}}

\int_{- π}^{π} sin (2 x) sin (2 x) d x

\frac{d}{d x} (- \frac{1}{1 - x ^{2}})

\int x^{2} 5 x + 5 d x

\int \frac{5}{33 x} x^{4} d x

t \to 0 lim (- 2 t)

What is (\partial)/(\partial x)((10-x^3-y^2)/(12x)) ?
The answer to (\partial)/(\partial x)((10-x^3-y^2)/(12x)) is (-2x^3+y^2-10)/(12x^2)