What is the d/(dz)(z^5-e^zln(z)) ?

The d/(dz)(z^5-e^zln(z)) is 5z^4-e^zln(z)-(e^z)/z

What is the first d/(dz)(z^5-e^zln(z)) ?

The first d/(dz)(z^5-e^zln(z)) is 5z^4-e^zln(z)-(e^z)/z

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\frac{d}{d z} (z^{5} - e^{z} ln (z))

5 z^{4} - e^{z} ln (z) - \frac{e ^{z}}{z}

Solution steps

\frac{d}{d z} (z^{5} - e^{z} ln (z))

Apply the Sum/Difference Rule:

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

= \frac{d}{d z} (z^{5}) - \frac{d}{d z} (e^{z} ln (z))

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

\frac{d}{d z} (e^{z} ln (z)) = e^{z} ln (z) + \frac{e ^{z}}{z}

= 5 z^{4} - (e^{z} ln (z) + \frac{e ^{z}}{z})

Simplify

= 5 z^{4} - e^{z} ln (z) - \frac{e ^{z}}{z}

What is the d/(dz)(z^5-e^zln(z)) ?
The d/(dz)(z^5-e^zln(z)) is 5z^4-e^zln(z)-(e^z)/z
What is the first d/(dz)(z^5-e^zln(z)) ?
The first d/(dz)(z^5-e^zln(z)) is 5z^4-e^zln(z)-(e^z)/z