What is the d/(dy)(e^{xy^2}) ?

The d/(dy)(e^{xy^2}) is e^{xy^2}*2xy

What is the first d/(dy)(e^{xy^2}) ?

The first d/(dy)(e^{xy^2}) is e^{xy^2}*2xy

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

e^{x y^{2}} \cdot 2 x y

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x y^{2}} \cdot 2 x y

\frac{d}{d x} (- \frac{2}{x})

3 x^{3} (1 + y^{2}) d x + x d y = 0

f (x) = 9 x^{4}

\int \frac{5 - x}{5 + x} d x

\int 12 (3 x + 1)^{3} d x