What is (\partial)/(\partial x)((3z+2)^5e^{(-x-5)}ln(4y-1)) ?

The answer to (\partial)/(\partial x)((3z+2)^5e^{(-x-5)}ln(4y-1)) is -e^{-x-5}ln(4y-1)(3z+2)^5

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(\partial)/(\partial x)((3z+2)^5e^{(-x-5)}ln(4y-1))

\frac{\partial}{\partial x} ((3 z + 2)^{5} e^{(- x - 5)} ln (4 y - 1))

- e^{- x - 5} ln (4 y - 1) (3 z + 2)^{5}

Solution steps

\frac{\partial}{\partial x} ((3 z + 2)^{5} e^{(- x - 5)} ln (4 y - 1))

Treat

z, y

as constants

Take the constant out:

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

= (3 z + 2)^{5} ln (4 y - 1) \frac{\partial}{\partial x} (e^{- x - 5})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x - 5) = - 1

= (3 z + 2)^{5} ln (4 y - 1) e^{- x - 5} (- 1)

Simplify

= - e^{- x - 5} ln (4 y - 1) (3 z + 2)^{5}

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What is (\partial)/(\partial x)((3z+2)^5e^{(-x-5)}ln(4y-1)) ?
The answer to (\partial)/(\partial x)((3z+2)^5e^{(-x-5)}ln(4y-1)) is -e^{-x-5}ln(4y-1)(3z+2)^5