What is the derivative of (x^2/(a^2)+(y^2)/(b^2)-1) ?

The derivative of (x^2/(a^2)+(y^2)/(b^2)-1) is (2x)/(a^2)+(2y\frac{dy)/(dx)}{b^2}

What is the first derivative of (x^2/(a^2)+(y^2)/(b^2)-1) ?

The first derivative of (x^2/(a^2)+(y^2)/(b^2)-1) is (2x)/(a^2)+(2y\frac{dy)/(dx)}{b^2}

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

\frac{2 x}{a ^{2}} + \frac{2 y \frac{d y}{d x}}{b ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= \frac{2 x}{a ^{2}} + \frac{2 y \frac{d y}{d x}}{b ^{2}} - 0

Simplify

= \frac{2 x}{a ^{2}} + \frac{2 y \frac{d y}{d x}}{b ^{2}}

y^{^{'}} = \frac{x}{6 y}

\frac{d y}{d t} = 0.12 - \frac{6 y}{50 - 2 t}

\int x sin (x + 1) d x

\int 3 tan^{2} (x) d x

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

What is the derivative of (x^2/(a^2)+(y^2)/(b^2)-1) ?
The derivative of (x^2/(a^2)+(y^2)/(b^2)-1) is (2x)/(a^2)+(2y\frac{dy)/(dx)}{b^2}
What is the first derivative of (x^2/(a^2)+(y^2)/(b^2)-1) ?
The first derivative of (x^2/(a^2)+(y^2)/(b^2)-1) is (2x)/(a^2)+(2y\frac{dy)/(dx)}{b^2}