What is (\partial)/(\partial x)(5e^{xy+7}) ?

The answer to (\partial)/(\partial x)(5e^{xy+7}) is 5e^{xy+7}y

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(\partial)/(\partial x)(5e^{xy+7})

\frac{\partial}{\partial x} (5 e^{x y + 7})

5 e^{x y + 7} y

Solution steps

\frac{\partial}{\partial x} (5 e^{x y + 7})

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (e^{x y + 7})

Apply the chain rule:

e^{x y + 7} \frac{\partial}{\partial x} (x y + 7)

= e^{x y + 7} \frac{\partial}{\partial x} (x y + 7)

\frac{\partial}{\partial x} (x y + 7) = y

= 5 e^{x y + 7} y

\int \frac{x ^{5}}{1 + x ^{3}} d x

\frac{\partial}{\partial y} (\frac{y}{( x + y + z )})

\int_{- 2}^{3} \frac{31}{x ^{4}} d x

\frac{d}{d x} (10)

2 e^{3 x} \frac{d y}{d x} = - \frac{6 x}{y ^{2}}

What is (\partial)/(\partial x)(5e^{xy+7}) ?
The answer to (\partial)/(\partial x)(5e^{xy+7}) is 5e^{xy+7}y