What is (\partial)/(\partial x)(1-(x/a)^2-(y/b)^2) ?

The answer to (\partial)/(\partial x)(1-(x/a)^2-(y/b)^2) is -(2x)/(a^2)

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(\partial)/(\partial x)(1-(x/a)^2-(y/b)^2)

\frac{\partial}{\partial x} (1 - (\frac{x}{a})^{2} - (\frac{y}{b})^{2})

- \frac{2 x}{a ^{2}}

Solution steps

\frac{\partial}{\partial x} (1 - (\frac{x}{a})^{2} - (\frac{y}{b})^{2})

Simplify

1 - (\frac{x}{a})^{2} - (\frac{y}{b})^{2} : 1 - \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}}

= \frac{\partial}{\partial x} (1 - \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}})

Treat

a, y, b

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (1) - \frac{\partial}{\partial x} (\frac{x ^{2}}{a ^{2}}) - \frac{\partial}{\partial x} (\frac{y ^{2}}{b ^{2}})

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (\frac{x ^{2}}{a ^{2}}) = \frac{2 x}{a ^{2}}

\frac{\partial}{\partial x} (\frac{y ^{2}}{b ^{2}}) = 0

= 0 - \frac{2 x}{a ^{2}} - 0

Simplify

= - \frac{2 x}{a ^{2}}

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x ^{2}})

\int \frac{1}{s ^{3} - 1} d s

\frac{d}{d x} (x arctan (2 x) - \frac{1}{4} ln (1 + 4 x^{2}))

9 x^{\frac{3}{5}} - 2 x^{\frac{6}{7}}, at x = 3

x \to - 4 lim (- (x^{2} + 10 x + 8))

What is (\partial)/(\partial x)(1-(x/a)^2-(y/b)^2) ?
The answer to (\partial)/(\partial x)(1-(x/a)^2-(y/b)^2) is -(2x)/(a^2)