What is (\partial)/(\partial x)(4e^{5xy}) ?

The answer to (\partial)/(\partial x)(4e^{5xy}) is 20e^{5xy}y

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(\partial)/(\partial x)(4e^{5xy})

\frac{\partial}{\partial x} (4 e^{5 x y})

20 e^{5 x y} y

Solution steps

\frac{\partial}{\partial x} (4 e^{5 x y})

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (e^{5 x y})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (5 x y) = 5 y

= 4 e^{5 x y} \cdot 5 y

Simplify

= 20 e^{5 x y} y

x \to + 0 lim (\frac{1}{csc ( x )})

\int \frac{1}{100 x ^{2} + 1} d x

y^{^{'}} = \frac{y}{x} + \frac{6 x ^{3}}{y} cos (x^{2})

y = 2 x + x^{2}, (- 2, 0)

\int x \cdot x d x

What is (\partial)/(\partial x)(4e^{5xy}) ?
The answer to (\partial)/(\partial x)(4e^{5xy}) is 20e^{5xy}y