What is the derivative of e^{(1-x^2-(y^2/4)}) ?

The derivative of e^{(1-x^2-(y^2/4)}) is e^{1-x^2-(y^2)/4}(-2x-(y(dy)/(dx))/2)

What is the first derivative of e^{(1-x^2-(y^2/4)}) ?

The first derivative of e^{(1-x^2-(y^2/4)}) is e^{1-x^2-(y^2)/4}(-2x-(y(dy)/(dx))/2)

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\frac{d}{d x} (e^{(1 - x^{2} - \frac{y ^{2}}{4})})

e^{1 - x^{2} - \frac{y ^{2}}{4}} (- 2 x - \frac{y \frac{d y}{d x}}{2})

Solution steps

\frac{d}{d x} (e^{(1 - x^{2} - \frac{y ^{2}}{4})})

Apply the chain rule:

e^{1 - x^{2} - \frac{y ^{2}}{4}} \frac{d}{d x} (1 - x^{2} - \frac{y ^{2}}{4})

= e^{1 - x^{2} - \frac{y ^{2}}{4}} \frac{d}{d x} (1 - x^{2} - \frac{y ^{2}}{4})

\frac{d}{d x} (1 - x^{2} - \frac{y ^{2}}{4}) = - 2 x - \frac{y \frac{d y}{d x}}{2}

= e^{1 - x^{2} - \frac{y ^{2}}{4}} (- 2 x - \frac{y \frac{d y}{d x}}{2})

e^{3 e^{x}}

f (x) = 2 x^{2}, at x = - 1

\int_{2}^{6} (\frac{1}{x - 2}) d x

x \to 1 lim (ln ∣ ln (x) ∣)

What is the derivative of e^{(1-x^2-(y^2/4)}) ?
The derivative of e^{(1-x^2-(y^2/4)}) is e^{1-x^2-(y^2)/4}(-2x-(y(dy)/(dx))/2)
What is the first derivative of e^{(1-x^2-(y^2/4)}) ?
The first derivative of e^{(1-x^2-(y^2/4)}) is e^{1-x^2-(y^2)/4}(-2x-(y(dy)/(dx))/2)