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

The answer to (\partial)/(\partial x)(cos(5z)e^{3x+4y}*3) is 9e^{3x+4y}cos(5z)

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

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 x + 4 y) = 3

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

Simplify

= 9 e^{3 x + 4 y} cos (5 z)

x \to 1 - lim (x ln (x))

y^{^{'}} - (2 x + 1) y + 3 x (5 x - 2) = 0

\frac{5}{x}, 1

\int_{2}^{7} \frac{1}{4 x + 8} d x

\int \frac{x + 1}{( x + 2 ) ( x - 3 )} d x

What is (\partial)/(\partial x)(cos(5z)e^{3x+4y}*3) ?
The answer to (\partial)/(\partial x)(cos(5z)e^{3x+4y}*3) is 9e^{3x+4y}cos(5z)