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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

- sin (5 z) \frac{\partial}{\partial z} (5 z)

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

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

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

Simplify

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

\int (1 + \frac{1}{t})^{3} (\frac{1}{t ^{2}}) d t

n = 1 \sum \infty (0.1)^{n}

\frac{d}{d x} (\frac{2 x + 5}{x ^{2} - 3})

f (x) = - 3 x + 4

(0, 0), (3, 4)

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