What is (\partial)/(\partial x)(e^{xyz^2+z}) ?

The answer to (\partial)/(\partial x)(e^{xyz^2+z}) is e^{xyz^2+z}yz^2

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(\partial)/(\partial x)(e^{xyz^2+z})

\frac{\partial}{\partial x} (e^{x y z^{2} + z})

e^{x y z^{2} + z} y z^{2}

Solution steps

\frac{\partial}{\partial x} (e^{x y z^{2} + z})

Treat

y, z

as constants

Apply the chain rule:

e^{x y z^{2} + z} \frac{\partial}{\partial x} (x y z^{2} + z)

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

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

= e^{x y z^{2} + z} y z^{2}

y^{^{''}} + 196 y = 0

\int x^{2} cosh (x) d x

\int \frac{5}{3 + 7 x ^{2}} d x

\int (cos (x)) (ln (sin (x))) d x

\frac{d}{d t} (\frac{t}{t ^{2} + 1})

What is (\partial)/(\partial x)(e^{xyz^2+z}) ?
The answer to (\partial)/(\partial x)(e^{xyz^2+z}) is e^{xyz^2+z}yz^2