What is (\partial)/(\partial x)(e^{-3t}sin(x+5t)) ?

The answer to (\partial)/(\partial x)(e^{-3t}sin(x+5t)) is e^{-3t}cos(x+5t)

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(\partial)/(\partial x)(e^{-3t}sin(x+5t))

\frac{\partial}{\partial x} (e^{- 3 t} sin (x + 5 t))

e^{- 3 t} cos (x + 5 t)

Solution steps

\frac{\partial}{\partial x} (e^{- 3 t} sin (x + 5 t))

Treat

t

as a constant

Take the constant out:

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

= e^{- 3 t} \frac{\partial}{\partial x} (sin (x + 5 t))

Apply the chain rule:

cos (x + 5 t) \frac{\partial}{\partial x} (x + 5 t)

= cos (x + 5 t) \frac{\partial}{\partial x} (x + 5 t)

\frac{\partial}{\partial x} (x + 5 t) = 1

= e^{- 3 t} cos (x + 5 t) \cdot 1

Simplify

= e^{- 3 t} cos (x + 5 t)

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

x \to 2 lim (\frac{x ^{3}}{2})

\int_{1}^{3} 1

y^{^{''}} - y = t^{2}

\frac{z}{( 1 - z ^{2} )}

What is (\partial)/(\partial x)(e^{-3t}sin(x+5t)) ?
The answer to (\partial)/(\partial x)(e^{-3t}sin(x+5t)) is e^{-3t}cos(x+5t)