What is (\partial)/(\partial x)(4e^{xy+3}) ?

The answer to (\partial)/(\partial x)(4e^{xy+3}) is 4e^{xy+3}y

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(\partial)/(\partial x)(4e^{xy+3})

\frac{\partial}{\partial x} (4 e^{x y + 3})

4 e^{x y + 3} y

Solution steps

\frac{\partial}{\partial x} (4 e^{x y + 3})

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (e^{x y + 3})

Apply the chain rule:

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

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

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

= 4 e^{x y + 3} y

(7 x^{6} + 2 x^{3})^{4}

x + 8

n = 0 \sum \infty 3^{n} 7^{- n}

\frac{\partial}{\partial y} (- x y^{2})

y = 2 x e^{- 6 x} - 4 e^{x^{3}}

What is (\partial)/(\partial x)(4e^{xy+3}) ?
The answer to (\partial)/(\partial x)(4e^{xy+3}) is 4e^{xy+3}y