What is the derivative of e^{xy^2} ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

- 6 x (2 e^{- 3 x^{2}})

(4 x) \cdot (3 x^{2})

8.1 \cdot 1 0^{- 6}

3^{x + 2}

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