What is (\partial)/(\partial x)(6e^{xy+4}) ?

The answer to (\partial)/(\partial x)(6e^{xy+4}) is 6e^{xy+4}y

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(\partial)/(\partial x)(6e^{xy+4})

\frac{\partial}{\partial x} (6 e^{x y + 4})

6 e^{x y + 4} y

Solution steps

\frac{\partial}{\partial x} (6 e^{x y + 4})

Treat

y

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (e^{x y + 4})

Apply the chain rule:

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

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

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

= 6 e^{x y + 4} y

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

\int (x^{2} - 9) e^{2 x} d x

\frac{d}{d x} ((2 x^{4} - 1) (5 x^{3} + 6 x))

2 sec^{2} (x)

\int \frac{x + 4}{x ^{2} + 2 x} d x

What is (\partial)/(\partial x)(6e^{xy+4}) ?
The answer to (\partial)/(\partial x)(6e^{xy+4}) is 6e^{xy+4}y