What is (\partial)/(\partial x)(4e^{xy+2}) ?

The answer to (\partial)/(\partial x)(4e^{xy+2}) is 4e^{xy+2}y

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(\partial)/(\partial x)(4e^{xy+2})

\frac{\partial}{\partial x} (4 e^{x y + 2})

4 e^{x y + 2} y

Solution steps

\frac{\partial}{\partial x} (4 e^{x y + 2})

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (e^{x y + 2})

Apply the chain rule:

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

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

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

= 4 e^{x y + 2} y

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\int cos^{3} (\frac{x}{17}) d x

\frac{d y}{d x}, sin (x y^{3}) = y^{3}

What is (\partial)/(\partial x)(4e^{xy+2}) ?
The answer to (\partial)/(\partial x)(4e^{xy+2}) is 4e^{xy+2}y