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

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

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

The first derivative of (x^2/(a^2)+(y^2)/(b^2)) 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}})

\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}})

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

\int (x (sin (x^{2}))) (cos^{8} (x^{2})) d x

\frac{d}{d x} (81 cos (3 x))

\frac{\partial}{\partial x} (x^{3} - 6 x^{2} - 34 x + 40)

f (x) = x (x - 3)

\frac{d}{d x} ((3 x - 1)^{4} (- 2 x + 9)^{5})

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