What is (\partial)/(\partial s)(te^{st}) ?

The answer to (\partial)/(\partial s)(te^{st}) is e^{ts}t^2

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(\partial)/(\partial s)(te^{st})

\frac{\partial}{\partial s} (t e^{s t})

e^{t s} t^{2}

Solution steps

\frac{\partial}{\partial s} (t e^{s t})

Treat

t

as a constant

Take the constant out:

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

= t \frac{\partial}{\partial s} (e^{s t})

Apply the chain rule:

e^{s t} \frac{\partial}{\partial s} (s t)

= e^{s t} \frac{\partial}{\partial s} (s t)

\frac{\partial}{\partial s} (s t) = t

= t e^{s t} t

Simplify

t e^{s t} t : e^{t s} t^{2}

= e^{t s} t^{2}

\int (t^{3}) (e^{- 2 t}) d t

\frac{d y}{d x} = x^{2} - y - 2

2 x, \frac{2}{x}, x = 3

\frac{\partial}{\partial y} (4 cos (x^{2} + y^{2}))

x \to 0 lim (\frac{ln ( 1 + 5 x )}{x})

What is (\partial)/(\partial s)(te^{st}) ?
The answer to (\partial)/(\partial s)(te^{st}) is e^{ts}t^2