What is (\partial)/(\partial z)(zln(x^2ycos(z))) ?

The answer to (\partial)/(\partial z)(zln(x^2ycos(z))) is ln(x^2ycos(z))-ztan(z)

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(\partial)/(\partial z)(zln(x^2ycos(z)))

\frac{\partial}{\partial z} (z ln (x^{2} y cos (z)))

ln (x^{2} y cos (z)) - z tan (z)

Solution steps

\frac{\partial}{\partial z} (z ln (x^{2} y cos (z)))

Treat

x, y

as constants

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = ln (x^{2} y cos (z))

= \frac{\partial}{\partial z} (z) ln (x^{2} y cos (z)) + \frac{\partial}{\partial z} (ln (x^{2} y cos (z))) z

\frac{\partial}{\partial z} (z) = 1

\frac{\partial}{\partial z} (ln (x^{2} y cos (z))) = - tan (z)

= 1 \cdot ln (x^{2} y cos (z)) + (- tan (z)) z

Simplify

= ln (x^{2} y cos (z)) - z tan (z)

\frac{\partial}{\partial x} (sin (x) + x cos (x))

\frac{d y}{d t} = 4 - \frac{1.5 y}{10 + 2.5 t}

\int 6 tan^{4} (x) d x

\frac{\partial}{\partial x} (2 x + y + 1)

\int \frac{3 x ^{2} - 7}{x ^{3} - 7 x + 6} d x

What is (\partial)/(\partial z)(zln(x^2ycos(z))) ?
The answer to (\partial)/(\partial z)(zln(x^2ycos(z))) is ln(x^2ycos(z))-ztan(z)