What is (\partial)/(\partial x)(2xe^{xy^3}) ?

The answer to (\partial)/(\partial x)(2xe^{xy^3}) is 2(e^{xy^3}+e^{xy^3}xy^3)

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(\partial)/(\partial x)(2xe^{xy^3})

\frac{\partial}{\partial x} (2 x e^{x y^{3}})

2 (e^{x y^{3}} + e^{x y^{3}} x y^{3})

Solution steps

\frac{\partial}{\partial x} (2 x e^{x y^{3}})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (x e^{x y^{3}})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x y^{3}}

= 2 (\frac{\partial}{\partial x} (x) e^{x y^{3}} + \frac{\partial}{\partial x} (e^{x y^{3}}) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{x y^{3}}) = e^{x y^{3}} y^{3}

= 2 (1 \cdot e^{x y^{3}} + e^{x y^{3}} y^{3} x)

Simplify

= 2 (e^{x y^{3}} + e^{x y^{3}} x y^{3})

36 - y^{2}

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (2 x) + 1

x \to + (- 1) - lim (2)

\frac{d}{d x} (- \frac{2 sec ^{2} ( x )}{( 1 + tan ( x ) ) ^{3}})

f (x) = \frac{7}{x}, at x = 1

What is (\partial)/(\partial x)(2xe^{xy^3}) ?
The answer to (\partial)/(\partial x)(2xe^{xy^3}) is 2(e^{xy^3}+e^{xy^3}xy^3)