What is the derivative of e^{y^2-x^2} ?

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

What is the first derivative of e^{y^2-x^2} ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

y^{^{''}} + y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int sec^{3} (5 x) tan^{5} (5 x) d x

f (x) = 16 x, at x = 4

\int_{3}^{2} (5 x^{2} + 4 x + 9) d x

y^{^{''}} + 4 y = 5 sec (2 t)

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