What is (\partial)/(\partial x)(-9e^{-5xy}) ?

The answer to (\partial)/(\partial x)(-9e^{-5xy}) is 45e^{-5xy}y

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(\partial)/(\partial x)(-9e^{-5xy})

\frac{\partial}{\partial x} (- 9 e^{- 5 x y})

45 e^{- 5 x y} y

Solution steps

\frac{\partial}{\partial x} (- 9 e^{- 5 x y})

Treat

y

as a constant

Take the constant out:

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

= - 9 \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

= - 9 e^{- 5 x y} (- 5 y)

Simplify

= 45 e^{- 5 x y} y

\int_{0}^{\frac{π}{6}} cos^{2} (3 x) d x

\int cot^{3} (8 x) d x

\int \frac{3}{2} sin (x) d x

y = 40 (x^{2} - 2 x)

f (x) = 2 x^{2} - 5 x + 3, at a = 1

What is (\partial)/(\partial x)(-9e^{-5xy}) ?
The answer to (\partial)/(\partial x)(-9e^{-5xy}) is 45e^{-5xy}y