What is (\partial)/(\partial x)(5e^{xy+6}) ?

The answer to (\partial)/(\partial x)(5e^{xy+6}) is 5e^{xy+6}y

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(\partial)/(\partial x)(5e^{xy+6})

\frac{\partial}{\partial x} (5 e^{x y + 6})

5 e^{x y + 6} y

Solution steps

\frac{\partial}{\partial x} (5 e^{x y + 6})

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (e^{x y + 6})

Apply the chain rule:

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

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

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

= 5 e^{x y + 6} y

y^{^{''}} + 2 y^{^{'}} + y = 6 e^{- t}

\int \frac{1}{4} e^{- 2 x} d x

f (x) = 4 x^{2} - 5 x + 2

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

\frac{d}{d x} (x^{2} e^{- \frac{1}{x}})

What is (\partial)/(\partial x)(5e^{xy+6}) ?
The answer to (\partial)/(\partial x)(5e^{xy+6}) is 5e^{xy+6}y