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

The d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) is -5e^{3{x}+4{y}}sin(5{z})

What is the first d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) ?

The first d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) is -5e^{3{x}+4{y}}sin(5{z})

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) ?
The d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) is -5e^{3{x}+4{y}}sin(5{z})
What is the first d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) ?
The first d/(d{z)}(e^{3{x}+4{y}}cos(5{z})) is -5e^{3{x}+4{y}}sin(5{z})