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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

\frac{4}{3} π (\frac{0.16}{4 π ( 0.2 )})^{3}

1 \cdot 1 0^{- 12} (e^{\frac{0.7}{0.025}} - 1)

(4 π \cdot 8.85 \cdot 1 0^{- 12} \cdot 25 \cdot 1 0^{- 4}) \cdot 0.036

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

6 e^{- 3 x} \cdot (e^{x} - 1)

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