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Popular >

(\partial)/(\partial x)(e^{-x}sin(y)z)

Solution

\frac{\partial}{\partial x} (e^{- x} sin (y) z)

Solution

- e^{- x} z sin (y)

Solution steps

\frac{\partial}{\partial x} (e^{- x} sin (y) z)

Treat

y, z

as constants

Take the constant out:

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

= sin (y) z \frac{\partial}{\partial x} (e^{- x})

Apply the chain rule:

e^{- x} \frac{\partial}{\partial x} (- x)

= e^{- x} \frac{\partial}{\partial x} (- x)

\frac{\partial}{\partial x} (- x) = - 1

= sin (y) z e^{- x} (- 1)

Simplify

= - e^{- x} z sin (y)

Popular Examples

sum from n=1 to infinity of (3n)/(6n+13)

n = 1 \sum \infty \frac{3 n}{6 n + 13}

integral of 1/(xln^2(x))

\int \frac{1}{x ln ^{2} ( x )} d x

f (x) = cos (4 x + 1)

integral from-2 to 0 of (4-x)

\int_{- 2}^{0} (4 - x) d x

(\partial)/(\partial x)((e^x)/(1+e^x))

\frac{\partial}{\partial x} (\frac{e ^{x}}{1 + e ^{x}})

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(e^{-x}sin(y)z) ?
The answer to (\partial)/(\partial x)(e^{-x}sin(y)z) is -e^{-x}zsin(y)