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

The answer to (\partial)/(\partial z)(-5e^{3x+4y}sin(5z)) is -25e^{3x+4y}cos(5z)

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

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

- 25 e^{3 x + 4 y} cos (5 z)

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

cos (5 z) \frac{\partial}{\partial z} (5 z)

= cos (5 z) \frac{\partial}{\partial z} (5 z)

\frac{\partial}{\partial z} (5 z) = 5

= - 5 e^{3 x + 4 y} cos (5 z) \cdot 5

Simplify

= - 25 e^{3 x + 4 y} cos (5 z)

\int (e^{x} - x^{e}) d x

4 t e^{- 3 t}

x \to - \infty lim (\frac{6 x ^{2} + 5 x ^{\frac{1}{3}}}{9 x ^{4} + 7})

n = 1 \sum \infty n^{n} x^{n}

y^{^{'}} + 8 (tan (8 x)) y = - 5 cos (8 x)

What is (\partial)/(\partial z)(-5e^{3x+4y}sin(5z)) ?
The answer to (\partial)/(\partial z)(-5e^{3x+4y}sin(5z)) is -25e^{3x+4y}cos(5z)