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

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

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

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

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

e^{x} cos (y) + y z

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x y z) = y z

\frac{d}{d x} (\frac{5 z ^{4}}{4}) = 0

\frac{d}{d x} (e^{x} cos (y)) = cos (y) e^{x}

= y z + 0 + cos (y) e^{x}

Simplify

= e^{x} cos (y) + y z

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