What is (\partial)/(\partial x)(sin(nx)e^{-n^2t}) ?

The answer to (\partial)/(\partial x)(sin(nx)e^{-n^2t}) is e^{-n^2t}cos(nx)n

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(\partial)/(\partial x)(sin(nx)e^{-n^2t})

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

e^{- n^{2} t} cos (n x) n

Solution steps

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

Treat

n, t

as a constant

Take the constant out:

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

= e^{- n^{2} t} \frac{\partial}{\partial x} (sin (n x))

Apply the chain rule:

cos (n x) \frac{\partial}{\partial x} (n x)

= cos (n x) \frac{\partial}{\partial x} (n x)

\frac{\partial}{\partial x} (n x) = n

= e^{- n^{2} t} cos (n x) n

x \to \infty lim (1 - e^{x})

x \to - 1 lim (x^{2} + 4)

\int \frac{1}{5 + 2 x} d x

\int x - 9 cos (x) d x

y = \frac{5}{x}, y = \frac{5}{x ^{2}}, x = 6

What is (\partial)/(\partial x)(sin(nx)e^{-n^2t}) ?
The answer to (\partial)/(\partial x)(sin(nx)e^{-n^2t}) is e^{-n^2t}cos(nx)n